3680:
3668:
5219:
37:
5528:
7462:
531:
series from above.) Applying this to the geometric progression 31, 62, 124, 248, 496 (which results from 1, 2, 4, 8, 16 by multiplying all terms by 31), we see that 62 minus 31 is to 31 as 496 minus 31 is to the sum of 31, 62, 124, 248. Therefore, the numbers 1, 2, 4, 8, 16, 31, 62, 124 and 248 add up to 496 and further these are all the numbers that
530:
Book IX, Proposition 35, proves that in a geometric series if the first term is subtracted from the second and last term in the sequence, then as the excess of the second is to the first—so is the excess of the last to all those before it. (This is a restatement of our formula for geometric
2176:
All of these numbers over 4 end with the digit 6. Starting with 16 the last two digits are periodic with period 4, with the cycle 16–56–36–96–, and starting with 16 the last three digits are periodic with period 20. These patterns are generally true of any power, with respect to
3302:
2 is the largest known power of two containing the least number of zeros relative to its power. It is conjectured by Metin
Sariyar that every digit 0 to 9 is inclined to appear an equal number of times in the decimal expansion of power of two as the power increases. (sequence
2454:
1125:
Starting with 2 the last digit is periodic with period 4, with the cycle 2–4–8–6–, and starting with 4 the last two digits are periodic with period 20. These patterns are generally true of any power, with respect to any
4066:
3580:
2726:. The space of all possible colors, 16,777,216, can be determined by 16 (6 digits with 16 possible values for each), 256 (3 channels with 256 possible values for each), or 2 (24 bits with 2 possible values for each).
432:
Numbers that are not powers of two occur in a number of situations, such as video resolutions, but they are often the sum or product of only two or three powers of two, or powers of two minus one. For example,
3683:
The sum of powers of two from zero to a given power, inclusive, is 1 less than the next power of two, whereas the sum of powers of two from minus-infinity to a given power, inclusive, equals the next power of
4618:
527:. For example, the sum of the first 5 terms of the series 1 + 2 + 4 + 8 + 16 = 31, which is a prime number. The sum 31 multiplied by 16 (the 5th term in the series) equals 496, which is a perfect number.
2304:
349:. Either way, one less than a power of two is often the upper bound of an integer in binary computers. As a consequence, numbers of this form show up frequently in computer software. As an example, a
4440:
3515:
4790:
4836:
4278:
2777:
is measured in seconds since
January 1, 1970, it will run out at 2,147,483,647 seconds or 03:14:07 UTC on Tuesday, 19 January 2038 on 32-bit computers running Unix, a problem known as the
4160:
3057:, where the first square contains one grain of rice and each succeeding square twice as many as the previous square. For this reason the number is sometimes known as the "chess number".
5410:
3871:
3645:
5564:
4974:
4498:
429:, at least one of the sector size, number of sectors per track, and number of tracks per surface is a power of two. The logical block size is almost always a power of two.
2258:
4196:
3926:
5400:
2289:
5005:
5053:
4210:
4897:
Though they vary in word size, all x86 processors use the term "word" to mean 16 bits; thus, a 32-bit x86 processor refers to its native wordsize as a dword
1370:
It takes approximately 17 powers of 1024 to reach 50% deviation and approximately 29 powers of 1024 to reach 100% deviation of the same powers of 1000. Also see
4089:
3893:
1174:
The first few powers of 2 are slightly larger than those same powers of 1000 (10). The powers of 2 values that have less than 27% deviation are listed below:
5493:
4202:
5334:
3934:
3359:
3310:
3276:
3236:
3196:
3077:
2201:
1422:
1168:
1150:
608:
164:
5557:
3520:
7498:
3372:
1386:
Because data (specifically integers) and the addresses of data are stored using the same hardware, and the data is stored in one or more octets (
5344:
3341:
2939:
4984:
3712:. It is also the sums of the cardinalities of certain subsets: the subset of integers with no 1s (consisting of a single number, written as
5339:
4879:
3728:
and the number of 1s being considered (for example, there are 10-choose-3 binary numbers with ten digits that include exactly three 1s).
6364:
5550:
2487:
distinct values, which can either be regarded as mere bit-patterns, or are more commonly interpreted as the unsigned numbers from 0 to
6359:
5508:
5099:
5046:
4907:
4507:
6374:
6354:
2449:{\displaystyle \sum _{i=0}^{\infty }{\frac {1}{2^{2^{i}}x_{i}}}={\frac {1}{2x_{0}}}+{\frac {1}{4x_{1}}}+{\frac {1}{16x_{2}}}+\cdots }
7772:
5488:
5390:
5380:
4865:
4728:
4697:
574:
4287:. The powers of 2 are the natural numbers greater than 1 that can be written as the sum of four square numbers in the fewest ways.
7067:
6647:
5498:
367:
2979:
2 − 1, a common maximum value (equivalently the number of positive values) for a signed 64-bit integer in programming languages.
4284:
6369:
3149:
3025:
2829:
2633:
7153:
371:
the main character was limited to carrying 255 rupees (the currency of the game) at any given time, and the video game
7807:
7687:
7592:
7587:
7582:
7577:
7572:
7567:
7562:
7557:
5503:
5405:
5039:
3257:
3040:
2848:
2653:
407:
346:
31:
7692:
7622:
6469:
4353:
3465:
353:
running on an 8-bit system might limit the score or the number of items the player can hold to 255—the result of using a
7682:
6819:
6138:
5931:
5531:
5001:
3323:
3289:
3054:
376:
312:
6854:
6824:
6499:
6489:
4745:
519:
terms of this progression is a prime number (and thus is a
Mersenne prime as mentioned above), then this sum times the
7491:
6995:
6409:
6143:
6123:
5513:
3021:
2825:
2637:
1391:
7637:
6685:
4794:
3163:, which means that 128-32=96 bits are available for addresses (as opposed to network designation). Thus, 2 addresses.
6849:
5385:
5375:
5365:
4934:
4226:
7871:
7866:
7782:
6944:
6567:
6324:
6133:
6115:
6009:
5999:
5989:
5395:
3385:
2820:
320:
6829:
4100:
7767:
7632:
7072:
6617:
6238:
6024:
6019:
6014:
6004:
5981:
4636:
3269:
The largest known power of 2 not containing all decimal digits (the digit 2 is missing in this case). (sequence
7845:
6057:
3679:
3460:
3327:
3293:
2949:
2859:
6314:
7183:
7148:
6934:
6844:
6718:
6693:
6602:
6592:
6204:
6186:
6106:
5480:
5302:
3822:
3145:
2878:
2718:) inclusive. This gives 8 bits for each channel, or 24 bits in total; for example, pure black is
7840:
7735:
7484:
7443:
6713:
6587:
6218:
5994:
5774:
5701:
5142:
5089:
4303:
2261:
470:
264:
4648:
3601:
7802:
7792:
7730:
6698:
6552:
6479:
5634:
5349:
5094:
3732:
502:
498:
72:
7407:
7047:
3318:
115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936
7340:
7234:
7198:
6939:
6662:
6642:
6459:
6128:
5916:
5888:
5460:
5297:
5066:
3693:
3672:
2710:
system, where colors are defined by three values (red, green and blue) independently ranging from 0 (
2463:. Despite the rapid growth of this sequence, it is the slowest-growing irrationality sequence known.
2296:
2186:
1135:
510:
3667:
7881:
7677:
7062:
6926:
6921:
6889:
6652:
6627:
6622:
6597:
6527:
6523:
6454:
6344:
6176:
5972:
5941:
5440:
5307:
4653:
4457:
3671:
As each increase in dimension doubles the number of shapes, the sum of coefficients on each row of
2906:, or 1,000,000,000,000 multiplier, which causes a change of prefix. For example, 1,099,511,627,776
2500:
686:
7461:
561:
cannot divide 16 or it would be amongst the numbers 1, 2, 4, 8 or 16. Therefore, 31 cannot divide
382:
Powers of two are often used to measure computer memory. A byte is now considered eight bits (an
7725:
7465:
7219:
7214:
7128:
7102:
7000:
6979:
6751:
6632:
6582:
6504:
6474:
6414:
6181:
6161:
6092:
5805:
5281:
5266:
5238:
5218:
5157:
3648:
419:
87:
7627:
7617:
6349:
5370:
5018:
4720:
4714:
3299:
2 = 862,718,293,348,820,473,429,344,482,784,628,181,556,388,621,521,298,319,395,315,527,974,912
2229:
7876:
7359:
7304:
7158:
7133:
7107:
6884:
6562:
6557:
6484:
6464:
6449:
6171:
6153:
6072:
6062:
6047:
5825:
5810:
5470:
5271:
5243:
5197:
5187:
5167:
5152:
4980:
4861:
4851:
4724:
4693:
4168:
3776:
3656:
3587:
2778:
2538:
2460:
383:
358:
3898:
402:, may be, and has traditionally been, used, to mean 1,024 (2). However, in general, the term
283:. Written in binary, a power of two always has the form 100...000 or 0.00...001, just like a
7647:
7597:
7395:
7188:
6774:
6746:
6736:
6728:
6612:
6577:
6572:
6539:
6233:
6196:
6087:
6082:
6077:
6067:
6039:
5926:
5878:
5873:
5830:
5769:
5455:
5276:
5202:
5192:
5172:
5074:
4915:
4871:
4658:
3652:
3449:
3398:
3060:
2 − 1 is also the number of moves required to complete the legendary 64-disk version of the
3006:
3002:
2998:
2994:
2990:
2986:
2889:
2808:
2804:
2800:
2796:
2730:
2700:
2618:
2614:
2582:
2292:
2218:
280:
2743:, or 1,000,000,000 multiplier, which causes a change of prefix. For example, 1,073,741,824
2267:
1358:
1 267 650 600 228 229 401 496 703 205 376
7787:
7371:
7260:
7193:
7119:
7042:
7016:
6834:
6547:
6404:
6339:
6309:
6299:
6294:
5960:
5868:
5815:
5659:
5599:
5233:
5162:
4875:
4857:
4451:
3595:
3345:
3229:
The largest known power of 2 not containing a pair of consecutive equal digits. (sequence
2660:
1371:
481:. The numbers that can be represented as sums of consecutive positive integers are called
478:
411:
3716:
0s), the subset with a single 1, the subset with two 1s, and so on up to the subset with
2673:, or 1,000,000 multiplier, which causes a change of prefix. For example: 1,048,576
7817:
7708:
7642:
7607:
7376:
7244:
7229:
7093:
7057:
7032:
6908:
6879:
6864:
6741:
6637:
6607:
6334:
6289:
6166:
5764:
5759:
5754:
5726:
5711:
5624:
5609:
5587:
5574:
5465:
5450:
5445:
5124:
5109:
4847:
4663:
4074:
3878:
3804:
3430:
3422:
3061:
2165:
1503:
1375:
1094:
1066:
678:
524:
454:
103:
64:
461:
is a
Mersenne prime because it is 1 less than 32 (2). Similarly, a prime number (like
36:
7860:
7777:
7552:
7532:
7507:
7299:
7283:
7224:
7178:
6874:
6859:
6769:
6494:
6052:
5921:
5883:
5840:
5721:
5706:
5696:
5654:
5644:
5619:
5430:
5104:
3591:
3112:, or 1,000,000,000,000,000,000,000,000 multiplier. 1,208,925,819,614,629,174,706,176
2789:
2763:
2629:
2516:
2157:
1038:
1010:
982:
954:
506:
482:
276:
41:
2549:
rather than the strict definition of an 8-bit quantity, as demonstrated by the term
7335:
7324:
7239:
7077:
7052:
6969:
6869:
6839:
6814:
6798:
6703:
6670:
6419:
6393:
6304:
6243:
5820:
5716:
5649:
5629:
5435:
5177:
4955:
4632:
3414:
3249:
3141:
3047:
3017:
2893:
2855:
2696:
1487:
926:
898:
870:
466:
462:
450:
154:
150:
146:
2483:
of that type. For example, a 32-bit word consisting of 4 bytes can represent
1341:
1 237 940 039 285 380 274 899 124 224
7822:
7762:
7294:
7169:
6974:
6438:
6329:
6284:
6279:
6029:
5936:
5835:
5664:
5639:
5614:
5182:
5129:
4668:
4061:{\displaystyle \sum _{k=0}^{n-1}2^{k}=2^{0}+2^{1}+2^{2}+\cdots +2^{n-1}=2^{n}-1}
3739:
3705:
3438:
3426:
3418:
3344:(hence the maximum number that can be represented by many programs, for example
2563:, or 1,000 multiplier, which causes a change of prefix. For example: 1,024
1471:
842:
814:
786:
474:
458:
284:
142:
138:
134:
30:"Power of 2" redirects here. For other uses of this and of "Power of two", see
7827:
7612:
7431:
7412:
6708:
6319:
4291:
4206:
3575:{\displaystyle {\frac {\log 3}{\log 2}}=1.5849\ldots \approx {\frac {19}{12}}}
3406:
3402:
3131:
2870:
1455:
1439:
758:
730:
702:
670:
426:
350:
342:
5542:
3284:
6,277,101,735,386,680,763,835,789,423,207,666,416,102,355,444,464,034,512,896
3090:, or 1,000,000,000,000,000,000,000 multiplier. 1,180,591,620,717,411,303,424
2938:
The number until which all integer values can exactly be represented in IEEE
17:
7718:
7713:
7547:
7037:
6964:
6956:
6761:
6675:
5793:
5114:
3784:
3743:
3445:
3410:
3117:
3095:
2877:. Although this is a seemingly large number, the number of available 32-bit
2774:
2586:
2520:
2472:
2161:
3724:
1s). Each of these is in turn equal to the binomial coefficient indexed by
394:, typically of 5 to 32 bits, rather than only an 8-bit unit.) The prefix
7652:
7138:
5062:
4930:
4690:
Schaum's
Outline of Theory and Problems of Essential Computer Mathematics
4639:
when probabilities of the source symbols are all negative powers of two.
3583:
3121:
3099:
2929:
2911:
2752:
2748:
2682:
2678:
2572:
2568:
2550:
2479:
which is a power of two, these numbers count the number of representable
1324:
1 208 925 819 614 629 174 706 176
184:
172:
80:
7542:
7143:
6802:
5031:
4217:
2967:
532:
372:
288:
60:
3189:
The largest known power of 2 not containing a 9 in decimal. (sequence
2962:, or 1,000,000,000,000,000,000 multiplier. 1,152,921,504,606,846,976
2729:
The size of the largest unsigned integer or address in computers with
7797:
7602:
7537:
3453:
3109:
3087:
2607:
2213:
4928:
Weisstein, Eric W. "Zero." From MathWorld--A Wolfram Web
Resource.
3265:
374,144,419,156,711,147,060,143,317,175,368,453,031,918,731,001,856
2863:
2467:
Powers of two whose exponents are powers of two in computer science
2921:
2903:
2740:
2692:
2670:
2560:
2178:
1127:
35:
2942:. Also the first power of 2 to start with the digit 9 in decimal.
425:
Powers of two occur in a range of other places as well. For many
40:
Visualization of powers of two from 1 to 1024 (2 to 2) as base-2
7476:
4613:{\displaystyle a^{2n}+b^{2n}=(a^{n}+b^{n}i)\cdot (a^{n}-b^{n}i)}
3253:
3134:
to be the largest power of two not containing a zero in decimal.
3113:
3091:
2963:
2959:
2925:
2907:
2882:
2874:
2744:
2674:
2564:
2542:
2534:
1307:
1 180 591 620 717 411 303 424
354:
7480:
7429:
7393:
7357:
7321:
7281:
6906:
6795:
6521:
6436:
6391:
6268:
5958:
5905:
5857:
5791:
5743:
5681:
5585:
5546:
5035:
2172:
Last digits for powers of two whose exponents are powers of two
593:
is not amongst the numbers 1, 2, 4, 8, 16, 31, 62, 124 or 248.
422:
have sizes that are powers of two, 32 or 64 being very common.
7527:
3070:
The first power of 2 to contain all decimal digits. (sequence
3010:
2976:
The number of non-negative values for a signed 64-bit integer.
2833:
2812:
2707:
2641:
2622:
2546:
2530:
2181:. The pattern continues where each pattern has starting point
1130:. The pattern continues where each pattern has starting point
581:
must divide 16 and be among the numbers 1, 2, 4, 8 or 16. Let
391:
386:), resulting in the possibility of 256 values (2). (The term
308:
2948:
The number of different possible keys in the obsolete 56 bit
2924:, or 1,000,000,000,000,000 multiplier. 1,125,899,906,842,624
3456:. In this case, the corresponding notes have the same name.
465:) that is one more than a positive power of two is called a
110:
times. The first ten powers of 2 for non-negative values of
3305:
3271:
3231:
3191:
3072:
2208:
Facts about powers of two whose exponents are powers of two
1417:
1163:
603:
485:; they are exactly the numbers that are not powers of two.
159:
441:. Put another way, they have fairly regular bit patterns.
505:, 1, 10, 100, 1000, 10000, 100000, ... ) is important in
171:
By comparison, powers of two with negative exponents are
130:
126:
122:
118:
68:
3647:, correct to about 0.1%. The just fifth is the basis of
2985:
The number of distinct values representable in a single
2795:
The number of distinct values representable in a single
2613:
The number of distinct values representable in a single
539:
divides 496 and it is not amongst these numbers. Assume
3001:
processor. Or, the number of values representable in a
2993:
processor. Or, the number of values representable in a
2803:
processor. Or, the number of values representable in a
1290:
1 152 921 504 606 846 976
345:
integer values can be positive, negative and zero; see
3837:
3486:
5411:
1/2 + 1/3 + 1/5 + 1/7 + 1/11 + ⋯ (inverses of primes)
5401:
1 − 1 + 2 − 6 + 24 − 120 + ⋯ (alternating factorials)
4797:
4748:
4510:
4460:
4356:
4283:
Every power of 2 (excluding 1) can be written as the
4229:
4171:
4103:
4077:
3937:
3901:
3881:
3825:
3604:
3523:
3468:
3429:
or otherwise modified notes have other durations. In
3053:
2 − 1, the number of grains of rice on a chessboard,
2706:
This number is the result of using the three-channel
2307:
2270:
2232:
589:
must be 124, which is impossible since by hypothesis
319:
can be arranged. A word, interpreted as an unsigned
7748:
7701:
7670:
7661:
7514:
7253:
7207:
7167:
7118:
7092:
7025:
7009:
6988:
6955:
6920:
6760:
6727:
6684:
6661:
6538:
6226:
6217:
6195:
6152:
6114:
6105:
6038:
5980:
5971:
5479:
5423:
5358:
5327:
5320:
5290:
5259:
5252:
5226:
5138:
5082:
5073:
4956:"Mersenne Prime Discovery - 2^82589933-1 is Prime!"
4435:{\displaystyle a^{n}+b^{n}=(a^{p})^{m}+(b^{p})^{m}}
4211:
sum of the reciprocals of the squared powers of two
3510:{\displaystyle 2^{7}\approx ({\tfrac {3}{2}})^{12}}
3322:The total number of different possible keys in the
3288:The total number of different possible keys in the
3244:
340,282,366,920,938,463,463,374,607,431,768,211,456
4908:"Powers of 2 Table - - - - - - Vaughn's Summaries"
4830:
4784:
4612:
4492:
4434:
4272:
4190:
4154:
4083:
4060:
3920:
3887:
3865:
3639:
3574:
3509:
3371:The maximum number that can fit in a 256-bit IEEE
3358:The maximum number that can fit in a 128-bit IEEE
2448:
2283:
2252:
4785:{\displaystyle \log _{1024/1000}1.5\approx 17.1,}
3340:The maximum number that can fit in a 64-bit IEEE
2499:. For more about representing signed numbers see
453:that is one less than a power of two is called a
361:, to store the number, giving a maximum value of
3441:of a fraction, is almost always a power of two.
2892:with domain equal to any 4-element set, such as
4831:{\displaystyle \log _{1024/1000}2\approx 29.2.}
1382:Powers of two whose exponents are powers of two
4273:{\displaystyle 2^{46}=70\ 368\ 744\ 177\ 664.}
2644:programming languages. The maximum range of a
1273:1 125 899 906 842 624
390:once meant (and in some cases, still means) a
191:times. Thus the first few powers of two where
7492:
5558:
5047:
3853:
3840:
1394:of two are common. The first 20 of them are:
8:
5494:Hypergeometric function of a matrix argument
4155:{\displaystyle 1+2^{1}+2^{2}+\cdots +2^{63}}
3731:Currently, powers of two are the only known
2491:, or as the range of signed numbers between
469:—the exponent itself is a power of two. A
5350:1 + 1/2 + 1/3 + ... (Riemann zeta function)
4719:. Oxford: Oxford University Press. p.
4203:sum of the reciprocals of the powers of two
3448:of two pitches is a power of two, then the
7667:
7499:
7485:
7477:
7426:
7390:
7354:
7318:
7278:
6952:
6917:
6903:
6792:
6535:
6518:
6433:
6388:
6265:
6223:
6111:
5977:
5968:
5955:
5902:
5859:Possessing a specific set of other numbers
5854:
5788:
5740:
5678:
5582:
5565:
5551:
5543:
5324:
5256:
5079:
5054:
5040:
5032:
4979:(2nd ed.). Springer. pp. 26–28.
4976:Number theory in science and communication
3137:2 = 79,228,162,514,264,337,593,543,950,336
3050:generally given to a single LAN or subnet.
2529:The number of values represented by the 8
1396:
1176:
613:
5406:1 + 1/2 + 1/3 + 1/4 + ⋯ (harmonic series)
5002:"O potęgach dwójki (About powers of two)"
4806:
4802:
4796:
4757:
4753:
4747:
4598:
4585:
4563:
4550:
4531:
4515:
4509:
4481:
4465:
4459:
4426:
4416:
4400:
4390:
4374:
4361:
4355:
4234:
4228:
4176:
4170:
4146:
4127:
4114:
4102:
4076:
4046:
4027:
4008:
3995:
3982:
3969:
3953:
3942:
3936:
3912:
3900:
3880:
3852:
3839:
3836:
3830:
3824:
3629:
3613:
3609:
3603:
3562:
3524:
3522:
3501:
3485:
3473:
3467:
3409:divided by a power of two; for example a
3360:quadruple-precision floating-point format
2431:
2418:
2406:
2393:
2381:
2368:
2356:
2344:
2339:
2329:
2323:
2312:
2306:
2275:
2269:
2242:
2237:
2231:
2202:Multiplicative group of integers modulo n
1151:Multiplicative group of integers modulo n
4216:The smallest natural power of two whose
3720:1s (consisting of the number written as
3678:
3666:
2769:The number of non-negative values for a
2595:The number of non-negative values for a
4893:
4891:
4889:
4850:(2004), "E24 Irrationality sequences",
4680:
3373:octuple-precision floating-point format
509:. Book IX, Proposition 36 of
4165:can be computed simply by evaluating:
3866:{\displaystyle 2^{x}{\tbinom {n}{x}}.}
3342:double-precision floating-point format
3258:universally unique identifiers (UUIDs)
3127:2 = 77,371,252,455,336,267,181,195,264
2940:double precision floating-point format
4285:sum of four square numbers in 24 ways
3105:2 = 1,208,925,819,614,629,174,706,176
1256:1 099 511 627 776
418: (Ki) meaning 1,024. Nearly all
7:
4692:. New York: McGraw-Hill. p. 3.
4504:>=1) can always be factorized as
3582:, closely relates the interval of 7
2519:of two. Also the first power of two
515:proves that if the sum of the first
501:1, 2, 4, 8, 16, 32, ... (or, in the
323:, can represent values from 0 (
5371:1 − 1 + 1 − 1 + ⋯ (Grandi's series)
4334:is even but not a power of 2, then
3819:-dimensional cross-polytope has is
3640:{\displaystyle 2^{7/12}\approx 3/2}
4853:Unsolved problems in number theory
3844:
3811:and the formula for the number of
2324:
259:, etc. Sometimes these are called
25:
7773:Indefinite and fictitious numbers
5489:Generalized hypergeometric series
4973:Manfred Robert Schroeder (2008).
3083:2 = 1,180,591,620,717,411,303,424
2879:IPv4 addresses has been exhausted
2537:, more specifically termed as an
2216:, these numbers are often called
575:fundamental theorem of arithmetic
488:
271:Base of the binary numeral system
7460:
7068:Perfect digit-to-digit invariant
5527:
5526:
5499:Lauricella hypergeometric series
5217:
5008:from the original on 2016-05-09.
3108:The binary approximation of the
3086:The binary approximation of the
3009:processor, such as the original
2958:The binary approximation of the
2920:The binary approximation of the
2902:The binary approximation of the
2811:processor, such as the original
2739:The binary approximation of the
2669:The binary approximation of the
2621:processor, such as the original
2559:The binary approximation of the
2471:Since it is common for computer
457:. For example, the prime number
414:have been standardized, such as
365:. For example, in the original
5509:Riemann's differential equation
4937:from the original on 2013-06-01
4882:from the original on 2016-04-28
4198:(which is the "chess number").
3067:2 = 295,147,905,179,352,825,856
565:. And since 31 does not divide
473:that has a power of two as its
275:Because two is the base of the
4607:
4578:
4572:
4543:
4423:
4409:
4397:
4383:
3498:
3482:
3452:between those pitches is full
3256:. Also the number of distinct
2982:2 = 18,446,744,073,709,551,616
279:, powers of two are common in
27:Two raised to an integer power
1:
7688:Conway chained arrow notation
5907:Expressible via specific sums
5504:Modular hypergeometric series
5345:1/4 + 1/16 + 1/64 + 1/256 + ⋯
4493:{\displaystyle a^{2n}+b^{2n}}
3895:powers of two (starting from
3393:Powers of two in music theory
2973:2 = 9,223,372,036,854,775,808
2955:2 = 1,152,921,504,606,846,976
408:International System of Units
347:signed number representations
341:) inclusively. Corresponding
32:Power of two (disambiguation)
5023:Fundamental Data Compression
4094:Thus, the sum of the powers
4091:being any positive integer.
3704:-digit binary integers. Its
1239:1 073 741 824
307:, is the number of ways the
267:of a positive power of two.
6996:Multiplicative digital root
5514:Theta hypergeometric series
4713:Sewell, Michael J. (1997).
4688:Lipschutz, Seymour (1982).
3791:. Similarly, the number of
3437:, which can be seen as the
3405:have a duration equal to a
3152:notation, ISPs are given a
1363:
1346:
1329:
1312:
1295:
1278:
1261:
1244:
1227:
1210:
1193:
1113:
1107:
1101:
1093:
1085:
1079:
1073:
1065:
1057:
1051:
1045:
1037:
1029:
1023:
1017:
1009:
1001:
995:
989:
981:
973:
967:
961:
953:
945:
939:
933:
925:
917:
911:
905:
897:
889:
883:
877:
869:
861:
855:
849:
841:
833:
827:
821:
813:
805:
799:
793:
785:
777:
771:
765:
757:
749:
743:
737:
729:
721:
715:
709:
701:
693:
685:
677:
669:
7898:
7783:Largest known prime number
5396:Infinite arithmetic series
5340:1/2 + 1/4 + 1/8 + 1/16 + ⋯
5335:1/2 − 1/4 + 1/8 − 1/16 + ⋯
3700:. Consider the set of all
3386:largest known prime number
3055:according to the old story
2945:2 = 72,057,594,037,927,936
2787:
2761:
2699:, which is used by common
2605:
1357:
1340:
1323:
1306:
1289:
1272:
1255:
1238:
1221:
1204:
1187:
1114:9,223,372,036,854,775,808
1086:4,611,686,018,427,387,904
1058:2,305,843,009,213,693,952
1030:1,152,921,504,606,846,976
652:
640:
628:
445:Mersenne and Fermat primes
29:
7836:
7768:Extended real number line
7683:Knuth's up-arrow notation
7456:
7439:
7425:
7403:
7389:
7367:
7353:
7331:
7317:
7290:
7277:
7073:Perfect digital invariant
6916:
6902:
6810:
6791:
6648:Superior highly composite
6534:
6517:
6445:
6432:
6400:
6387:
6275:
6264:
5967:
5954:
5912:
5901:
5864:
5853:
5801:
5787:
5750:
5739:
5692:
5677:
5595:
5581:
5522:
5215:
5000:Paweł Strzelecki (1994).
4716:Mathematics Masterclasses
4637:lossless data compression
4213:(powers of four) is 1/3.
3655:and seven octaves is the
3651:; the difference between
2935:2 = 9,007,199,254,740,992
2917:2 = 1,125,899,906,842,624
2695:that can be displayed in
2253:{\displaystyle 2^{2^{n}}}
175:: for a negative integer
63:, that is, the result of
7693:Steinhaus–Moser notation
6686:Euler's totient function
6470:Euler–Jacobi pseudoprime
5745:Other polynomial numbers
4912:www.vaughns-1-pagers.com
4450:.) But in the domain of
4442:, which is divisible by
4191:{\displaystyle 2^{64}-1}
3461:mathematical coincidence
2733:registers or data buses.
2185:, and the period is the
1134:, and the period is the
1002:576,460,752,303,423,488
974:288,230,376,151,711,744
946:144,115,188,075,855,872
90:exponents are integers:
51:is a number of the form
6500:Somer–Lucas pseudoprime
6490:Lucas–Carmichael number
6325:Lazy caterer's sequence
5227:Properties of sequences
4310:is a power of two. (If
3921:{\displaystyle 1=2^{0}}
3433:the lower numeral, the
3146:local Internet registry
2854:The minimum range of a
2628:The maximum range of a
2515:The number that is the
918:72,057,594,037,927,936
890:36,028,797,018,963,968
862:18,014,398,509,481,984
299:Two to the exponent of
7736:Fast-growing hierarchy
6375:Wedderburn–Etherington
5775:Lucky numbers of Euler
5090:Arithmetic progression
4832:
4786:
4628:Negative powers of two
4614:
4494:
4436:
4274:
4218:decimal representation
4192:
4156:
4085:
4062:
3964:
3922:
3889:
3867:
3766:is the cardinality of
3733:almost perfect numbers
3685:
3676:
3641:
3576:
3511:
3028:programming languages.
2866:programming languages.
2836:programming languages.
2773:32-bit integer. Since
2589:-compatible processor.
2545:is often defined as a
2507:Selected powers of two
2450:
2328:
2285:
2262:irrationality sequence
2254:
2189:of 2 modulo
1138:of 2 modulo
834:9,007,199,254,740,992
806:4,503,599,627,370,496
778:2,251,799,813,685,248
750:1,125,899,906,842,624
535:496. For suppose that
398:, in conjunction with
265:multiplicative inverse
44:
7793:Long and short scales
7731:Grzegorczyk hierarchy
6663:Prime omega functions
6480:Frobenius pseudoprime
6270:Combinatorial numbers
6139:Centered dodecahedral
5932:Primary pseudoperfect
5481:Hypergeometric series
5095:Geometric progression
4833:
4787:
4615:
4495:
4437:
4275:
4193:
4157:
4086:
4063:
3938:
3923:
3890:
3875:The sum of the first
3868:
3694:binomial coefficients
3682:
3670:
3642:
3577:
3512:
3144:generally given to a
3043:programming language.
2899:2 = 1,099,511,627,776
2851:programming language.
2691:The number of unique
2656:programming language.
2451:
2308:
2286:
2284:{\displaystyle x_{i}}
2264:: for every sequence
2255:
2212:In a connection with
2166:lower hyperoperations
503:binary numeral system
499:geometric progression
406:has been used in the
277:binary numeral system
261:inverse powers of two
187:multiplied by itself
39:
7122:-composition related
6922:Arithmetic functions
6524:Arithmetic functions
6460:Elliptic pseudoprime
6144:Centered icosahedral
6124:Centered tetrahedral
5461:Trigonometric series
5253:Properties of series
5100:Harmonic progression
5004:(in Polish). Delta.
4795:
4746:
4508:
4458:
4354:
4227:
4169:
4101:
4075:
3935:
3899:
3879:
3823:
3602:
3521:
3466:
3248:The total number of
3140:The total number of
3046:The total number of
2869:The total number of
2305:
2268:
2230:
2187:multiplicative order
1136:multiplicative order
1108:140,737,488,355,328
722:562,949,953,421,312
694:281,474,976,710,656
410:to mean 1,000 (10).
263:because each is the
7808:Orders of magnitude
7678:Scientific notation
7048:Kaprekar's constant
6568:Colossally abundant
6455:Catalan pseudoprime
6355:Schröder–Hipparchus
6134:Centered octahedral
6010:Centered heptagonal
6000:Centered pentagonal
5990:Centered triangular
5590:and related numbers
5441:Formal power series
4918:on August 12, 2015.
4624:is a power of two.
3330:(symmetric cipher).
3296:(symmetric cipher).
2663:on a 4-element set.
1398:
1392:double exponentials
1222:1 048 576
1178:
1080:70,368,744,177,664
1052:35,184,372,088,832
1024:17,592,186,044,416
615:
420:processor registers
379:at level 256.
86:Powers of two with
7726:Ackermann function
7466:Mathematics portal
7408:Aronson's sequence
7154:Smarandache–Wellin
6911:-dependent numbers
6618:Primitive abundant
6505:Strong pseudoprime
6495:Perrin pseudoprime
6475:Fermat pseudoprime
6415:Wolstenholme prime
6239:Squared triangular
6025:Centered decagonal
6020:Centered nonagonal
6015:Centered octagonal
6005:Centered hexagonal
5239:Monotonic function
5158:Fibonacci sequence
4828:
4782:
4610:
4490:
4432:
4338:can be written as
4270:
4188:
4152:
4081:
4058:
3918:
3885:
3863:
3858:
3686:
3677:
3653:twelve just fifths
3649:Pythagorean tuning
3637:
3572:
3507:
3495:
3384:One more than the
2547:collection of bits
2446:
2281:
2250:
1397:
1364:(26.8% deviation)
1347:(23.8% deviation)
1330:(20.9% deviation)
1313:(18.1% deviation)
1296:(15.3% deviation)
1279:(12.6% deviation)
1262:(10.0% deviation)
1177:
996:8,796,093,022,208
968:4,398,046,511,104
940:2,199,023,255,552
912:1,099,511,627,776
614:
573:measures 496, the
392:collection of bits
45:
7872:Integer sequences
7867:Binary arithmetic
7854:
7853:
7744:
7743:
7474:
7473:
7452:
7451:
7421:
7420:
7385:
7384:
7349:
7348:
7313:
7312:
7273:
7272:
7269:
7268:
7088:
7087:
6898:
6897:
6787:
6786:
6783:
6782:
6729:Aliquot sequences
6540:Divisor functions
6513:
6512:
6485:Lucas pseudoprime
6465:Euler pseudoprime
6450:Carmichael number
6428:
6427:
6383:
6382:
6260:
6259:
6256:
6255:
6252:
6251:
6213:
6212:
6101:
6100:
6058:Square triangular
5950:
5949:
5897:
5896:
5849:
5848:
5783:
5782:
5735:
5734:
5673:
5672:
5540:
5539:
5471:Generating series
5419:
5418:
5391:1 − 2 + 4 − 8 + ⋯
5386:1 + 2 + 4 + 8 + ⋯
5381:1 − 2 + 3 − 4 + ⋯
5376:1 + 2 + 3 + 4 + ⋯
5366:1 + 1 + 1 + 1 + ⋯
5316:
5315:
5244:Periodic sequence
5213:
5212:
5198:Triangular number
5188:Pentagonal number
5168:Heptagonal number
5153:Complete sequence
5075:Integer sequences
4986:978-3-540-85297-1
4649:Fermi–Dirac prime
4454:, the polynomial
4350:is odd, and thus
4306:, if and only if
4266:
4260:
4254:
4248:
4220:begins with 7 is
4084:{\displaystyle n}
3888:{\displaystyle n}
3851:
3675:is a power of two
3673:Pascal's triangle
3657:Pythagorean comma
3588:equal temperament
3570:
3548:
3494:
3401:, all unmodified
3388:as of June 2023.
2952:symmetric cipher.
2890:binary operations
2784:2 = 4,294,967,296
2779:year 2038 problem
2758:2 = 2,147,483,648
2736:2 = 1,073,741,824
2701:computer monitors
2461:irrational number
2438:
2413:
2388:
2363:
2293:positive integers
2154:
2153:
1368:
1367:
1245:(7.4% deviation)
1228:(4.9% deviation)
1211:(2.4% deviation)
1118:
1117:
75:and integer
16:(Redirected from
7889:
7668:
7598:Eddington number
7543:Hundred thousand
7501:
7494:
7487:
7478:
7464:
7427:
7396:Natural language
7391:
7355:
7323:Generated via a
7319:
7279:
7184:Digit-reassembly
7149:Self-descriptive
6953:
6918:
6904:
6855:Lucas–Carmichael
6845:Harmonic divisor
6793:
6719:Sparsely totient
6694:Highly cototient
6603:Multiply perfect
6593:Highly composite
6536:
6519:
6434:
6389:
6370:Telephone number
6266:
6224:
6205:Square pyramidal
6187:Stella octangula
6112:
5978:
5969:
5961:Figurate numbers
5956:
5903:
5855:
5789:
5741:
5679:
5583:
5567:
5560:
5553:
5544:
5530:
5529:
5456:Dirichlet series
5325:
5257:
5221:
5193:Polygonal number
5173:Hexagonal number
5146:
5080:
5056:
5049:
5042:
5033:
5026:
5016:
5010:
5009:
4997:
4991:
4990:
4970:
4964:
4963:
4960:www.mersenne.org
4952:
4946:
4945:
4943:
4942:
4926:
4920:
4919:
4914:. Archived from
4904:
4898:
4895:
4884:
4883:
4856:(3rd ed.),
4844:
4838:
4837:
4835:
4834:
4829:
4815:
4814:
4810:
4791:
4789:
4788:
4783:
4766:
4765:
4761:
4741:
4735:
4734:
4710:
4704:
4703:
4685:
4659:Binary logarithm
4654:Gould's sequence
4635:deliver optimal
4619:
4617:
4616:
4611:
4603:
4602:
4590:
4589:
4568:
4567:
4555:
4554:
4539:
4538:
4523:
4522:
4499:
4497:
4496:
4491:
4489:
4488:
4473:
4472:
4441:
4439:
4438:
4433:
4431:
4430:
4421:
4420:
4405:
4404:
4395:
4394:
4379:
4378:
4366:
4365:
4322:is divisible by
4279:
4277:
4276:
4271:
4264:
4258:
4252:
4246:
4239:
4238:
4197:
4195:
4194:
4189:
4181:
4180:
4161:
4159:
4158:
4153:
4151:
4150:
4132:
4131:
4119:
4118:
4090:
4088:
4087:
4082:
4067:
4065:
4064:
4059:
4051:
4050:
4038:
4037:
4013:
4012:
4000:
3999:
3987:
3986:
3974:
3973:
3963:
3952:
3927:
3925:
3924:
3919:
3917:
3916:
3894:
3892:
3891:
3886:
3872:
3870:
3869:
3864:
3859:
3857:
3856:
3843:
3835:
3834:
3818:
3814:
3810:
3802:
3798:
3790:
3782:
3771:
3765:
3763:
3755:
3751:
3727:
3723:
3719:
3715:
3711:
3703:
3699:
3691:
3663:Other properties
3646:
3644:
3643:
3638:
3633:
3622:
3621:
3617:
3581:
3579:
3578:
3573:
3571:
3563:
3549:
3547:
3536:
3525:
3516:
3514:
3513:
3508:
3506:
3505:
3496:
3487:
3478:
3477:
3444:If the ratio of
3399:musical notation
3380:
3367:
3354:
3336:
3319:
3308:
3285:
3274:
3266:
3252:available under
3245:
3234:
3225:
3223:
3221:
3219:
3217:
3215:
3213:
3211:
3209:
3207:
3205:
3203:
3194:
3185:
3183:
3181:
3179:
3177:
3175:
3173:
3171:
3169:
3167:
3161:
3160:
3157:
3075:
3039:variable in the
3020:variable in the
2858:variable in the
2847:variable in the
2846:
2842:
2824:variable in the
2823:
2818:The range of an
2725:
2722:, pure white is
2721:
2717:
2713:
2661:binary relations
2652:variable in the
2632:variable in the
2501:two's complement
2498:
2494:
2490:
2486:
2459:converges to an
2455:
2453:
2452:
2447:
2439:
2437:
2436:
2435:
2419:
2414:
2412:
2411:
2410:
2394:
2389:
2387:
2386:
2385:
2369:
2364:
2362:
2361:
2360:
2351:
2350:
2349:
2348:
2330:
2327:
2322:
2290:
2288:
2287:
2282:
2280:
2279:
2259:
2257:
2256:
2251:
2249:
2248:
2247:
2246:
2199:
2198:(5) = 4 × 5
2192:
2184:
2146:
2144:
2142:
2140:
2138:
2136:
2134:
2132:
2130:
2128:
2126:
2124:
2122:
2120:
2118:
2116:
2100:
2098:
2096:
2094:
2092:
2090:
2088:
2086:
2084:
2082:
2080:
2078:
2076:
2074:
2072:
2070:
2054:
2052:
2050:
2048:
2046:
2044:
2042:
2040:
2038:
2036:
2034:
2032:
2030:
2028:
2026:
2024:
2022:
2006:
2004:
2002:
2000:
1998:
1996:
1994:
1992:
1990:
1988:
1986:
1984:
1982:
1980:
1978:
1976:
1974:
1958:
1956:
1954:
1952:
1950:
1948:
1946:
1944:
1942:
1940:
1938:
1936:
1934:
1932:
1930:
1928:
1926:
1910:
1908:
1906:
1904:
1902:
1900:
1898:
1896:
1894:
1892:
1890:
1888:
1886:
1884:
1882:
1880:
1878:
1862:
1860:
1858:
1856:
1854:
1852:
1850:
1848:
1846:
1844:
1842:
1840:
1838:
1836:
1834:
1832:
1830:
1814:
1812:
1810:
1808:
1806:
1804:
1802:
1800:
1798:
1796:
1794:
1792:
1790:
1788:
1786:
1784:
1782:
1766:
1764:
1762:
1760:
1758:
1756:
1754:
1752:
1750:
1748:
1746:
1744:
1742:
1740:
1738:
1736:
1720:
1718:
1716:
1714:
1712:
1710:
1708:
1706:
1704:
1702:
1700:
1698:
1696:
1694:
1692:
1690:
1674:
1672:
1670:
1668:
1666:
1664:
1662:
1660:
1658:
1656:
1654:
1652:
1650:
1648:
1646:
1644:
1628:
1626:
1624:
1622:
1620:
1618:
1616:
1614:
1612:
1610:
1608:
1606:
1604:
1602:
1600:
1598:
1582:
1580:
1578:
1576:
1574:
1572:
1570:
1568:
1566:
1564:
1562:
1560:
1544:
1542:
1540:
1538:
1536:
1534:
1420:
1414:
1409:
1404:
1399:
1389:
1179:
1166:
1148:
1147:(5) = 4 × 5
1141:
1133:
884:549,755,813,888
856:274,877,906,944
828:137,438,953,472
662:
657:
650:
645:
638:
633:
626:
621:
616:
606:
592:
588:
584:
580:
572:
568:
564:
560:
556:
552:
548:
544:
538:
522:
518:
440:
436:
364:
340:
333:
329:
318:
306:
302:
295:Computer science
281:computer science
258:
256:
255:
252:
249:
242:
240:
239:
236:
233:
226:
224:
223:
220:
217:
210:
208:
207:
204:
201:
195:is negative are
194:
190:
182:
178:
162:
157:, ... (sequence
113:
109:
101:
97:
93:
78:
58:
54:
21:
7897:
7896:
7892:
7891:
7890:
7888:
7887:
7886:
7857:
7856:
7855:
7850:
7832:
7788:List of numbers
7756:
7754:
7752:
7750:
7740:
7697:
7663:
7657:
7628:Graham's number
7618:Skewes's number
7520:
7518:
7516:
7510:
7505:
7475:
7470:
7448:
7444:Strobogrammatic
7435:
7417:
7399:
7381:
7363:
7345:
7327:
7309:
7286:
7265:
7249:
7208:Divisor-related
7203:
7163:
7114:
7084:
7021:
7005:
6984:
6951:
6924:
6912:
6894:
6806:
6805:related numbers
6779:
6756:
6723:
6714:Perfect totient
6680:
6657:
6588:Highly abundant
6530:
6509:
6441:
6424:
6396:
6379:
6365:Stirling second
6271:
6248:
6209:
6191:
6148:
6097:
6034:
5995:Centered square
5963:
5946:
5908:
5893:
5860:
5845:
5797:
5796:defined numbers
5779:
5746:
5731:
5702:Double Mersenne
5688:
5669:
5591:
5577:
5575:natural numbers
5571:
5541:
5536:
5518:
5475:
5424:Kinds of series
5415:
5354:
5321:Explicit series
5312:
5286:
5248:
5234:Cauchy sequence
5222:
5209:
5163:Figurate number
5140:
5134:
5125:Powers of three
5069:
5060:
5030:
5029:
5017:
5013:
4999:
4998:
4994:
4987:
4972:
4971:
4967:
4954:
4953:
4949:
4940:
4938:
4929:
4927:
4923:
4906:
4905:
4901:
4896:
4887:
4868:
4860:, p. 346,
4858:Springer-Verlag
4848:Guy, Richard K.
4846:
4845:
4841:
4798:
4793:
4792:
4749:
4744:
4743:
4742:
4738:
4731:
4712:
4711:
4707:
4700:
4687:
4686:
4682:
4677:
4645:
4630:
4594:
4581:
4559:
4546:
4527:
4511:
4506:
4505:
4477:
4461:
4456:
4455:
4452:complex numbers
4422:
4412:
4396:
4386:
4370:
4357:
4352:
4351:
4230:
4225:
4224:
4172:
4167:
4166:
4142:
4123:
4110:
4099:
4098:
4073:
4072:
4042:
4023:
4004:
3991:
3978:
3965:
3933:
3932:
3928:) is given by,
3908:
3897:
3896:
3877:
3876:
3838:
3826:
3821:
3820:
3816:
3812:
3808:
3800:
3792:
3788:
3780:
3767:
3759:
3757:
3753:
3747:
3725:
3721:
3717:
3713:
3709:
3701:
3697:
3689:
3688:The sum of all
3665:
3605:
3600:
3599:
3596:just intonation
3537:
3526:
3519:
3518:
3497:
3469:
3464:
3463:
3431:time signatures
3395:
3378:
3365:
3352:
3346:Microsoft Excel
3334:
3317:
3304:
3283:
3270:
3264:
3243:
3230:
3190:
3158:
3155:
3154:
3071:
3031:The range of a
3016:The range of a
2844:
2840:
2839:The range of a
2819:
2792:
2766:
2723:
2719:
2715:
2711:
2610:
2599:16-bit integer.
2509:
2496:
2492:
2488:
2484:
2469:
2427:
2423:
2402:
2398:
2377:
2373:
2352:
2340:
2335:
2334:
2303:
2302:
2271:
2266:
2265:
2238:
2233:
2228:
2227:
2210:
2194:
2190:
2182:
2174:
1416:
1412:
1407:
1402:
1387:
1384:
1372:Binary prefixes
1194:(0% deviation)
1162:
1159:
1143:
1139:
1131:
1123:
800:68,719,476,736
772:34,359,738,368
744:17,179,869,184
660:
655:
648:
643:
636:
631:
624:
619:
602:
599:
597:Table of values
590:
586:
582:
578:
570:
566:
562:
558:
554:
550:
546:
540:
536:
520:
516:
495:
479:dyadic rational
447:
438:
434:
412:Binary prefixes
375:famously has a
368:Legend of Zelda
362:
339:
335:
331:
328:
324:
316:
304:
300:
297:
273:
253:
250:
247:
246:
244:
237:
234:
231:
230:
228:
221:
218:
215:
214:
212:
205:
202:
199:
198:
196:
192:
188:
180:
176:
158:
111:
107:
99:
95:
91:
76:
56:
52:
34:
28:
23:
22:
15:
12:
11:
5:
7895:
7893:
7885:
7884:
7879:
7874:
7869:
7859:
7858:
7852:
7851:
7849:
7848:
7843:
7837:
7834:
7833:
7831:
7830:
7825:
7820:
7818:Power of three
7815:
7810:
7805:
7800:
7798:Number systems
7795:
7790:
7785:
7780:
7775:
7770:
7765:
7759:
7757:
7753:(alphabetical
7746:
7745:
7742:
7741:
7739:
7738:
7733:
7728:
7723:
7722:
7721:
7716:
7709:Hyperoperation
7705:
7703:
7699:
7698:
7696:
7695:
7690:
7685:
7680:
7674:
7672:
7665:
7659:
7658:
7656:
7655:
7650:
7645:
7640:
7635:
7630:
7625:
7623:Moser's number
7620:
7615:
7610:
7608:Shannon number
7605:
7600:
7595:
7590:
7585:
7580:
7575:
7570:
7565:
7560:
7555:
7550:
7545:
7540:
7535:
7530:
7524:
7522:
7512:
7511:
7506:
7504:
7503:
7496:
7489:
7481:
7472:
7471:
7469:
7468:
7457:
7454:
7453:
7450:
7449:
7447:
7446:
7440:
7437:
7436:
7430:
7423:
7422:
7419:
7418:
7416:
7415:
7410:
7404:
7401:
7400:
7394:
7387:
7386:
7383:
7382:
7380:
7379:
7377:Sorting number
7374:
7372:Pancake number
7368:
7365:
7364:
7358:
7351:
7350:
7347:
7346:
7344:
7343:
7338:
7332:
7329:
7328:
7322:
7315:
7314:
7311:
7310:
7308:
7307:
7302:
7297:
7291:
7288:
7287:
7284:Binary numbers
7282:
7275:
7274:
7271:
7270:
7267:
7266:
7264:
7263:
7257:
7255:
7251:
7250:
7248:
7247:
7242:
7237:
7232:
7227:
7222:
7217:
7211:
7209:
7205:
7204:
7202:
7201:
7196:
7191:
7186:
7181:
7175:
7173:
7165:
7164:
7162:
7161:
7156:
7151:
7146:
7141:
7136:
7131:
7125:
7123:
7116:
7115:
7113:
7112:
7111:
7110:
7099:
7097:
7094:P-adic numbers
7090:
7089:
7086:
7085:
7083:
7082:
7081:
7080:
7070:
7065:
7060:
7055:
7050:
7045:
7040:
7035:
7029:
7027:
7023:
7022:
7020:
7019:
7013:
7011:
7010:Coding-related
7007:
7006:
7004:
7003:
6998:
6992:
6990:
6986:
6985:
6983:
6982:
6977:
6972:
6967:
6961:
6959:
6950:
6949:
6948:
6947:
6945:Multiplicative
6942:
6931:
6929:
6914:
6913:
6909:Numeral system
6907:
6900:
6899:
6896:
6895:
6893:
6892:
6887:
6882:
6877:
6872:
6867:
6862:
6857:
6852:
6847:
6842:
6837:
6832:
6827:
6822:
6817:
6811:
6808:
6807:
6796:
6789:
6788:
6785:
6784:
6781:
6780:
6778:
6777:
6772:
6766:
6764:
6758:
6757:
6755:
6754:
6749:
6744:
6739:
6733:
6731:
6725:
6724:
6722:
6721:
6716:
6711:
6706:
6701:
6699:Highly totient
6696:
6690:
6688:
6682:
6681:
6679:
6678:
6673:
6667:
6665:
6659:
6658:
6656:
6655:
6650:
6645:
6640:
6635:
6630:
6625:
6620:
6615:
6610:
6605:
6600:
6595:
6590:
6585:
6580:
6575:
6570:
6565:
6560:
6555:
6553:Almost perfect
6550:
6544:
6542:
6532:
6531:
6522:
6515:
6514:
6511:
6510:
6508:
6507:
6502:
6497:
6492:
6487:
6482:
6477:
6472:
6467:
6462:
6457:
6452:
6446:
6443:
6442:
6437:
6430:
6429:
6426:
6425:
6423:
6422:
6417:
6412:
6407:
6401:
6398:
6397:
6392:
6385:
6384:
6381:
6380:
6378:
6377:
6372:
6367:
6362:
6360:Stirling first
6357:
6352:
6347:
6342:
6337:
6332:
6327:
6322:
6317:
6312:
6307:
6302:
6297:
6292:
6287:
6282:
6276:
6273:
6272:
6269:
6262:
6261:
6258:
6257:
6254:
6253:
6250:
6249:
6247:
6246:
6241:
6236:
6230:
6228:
6221:
6215:
6214:
6211:
6210:
6208:
6207:
6201:
6199:
6193:
6192:
6190:
6189:
6184:
6179:
6174:
6169:
6164:
6158:
6156:
6150:
6149:
6147:
6146:
6141:
6136:
6131:
6126:
6120:
6118:
6109:
6103:
6102:
6099:
6098:
6096:
6095:
6090:
6085:
6080:
6075:
6070:
6065:
6060:
6055:
6050:
6044:
6042:
6036:
6035:
6033:
6032:
6027:
6022:
6017:
6012:
6007:
6002:
5997:
5992:
5986:
5984:
5975:
5965:
5964:
5959:
5952:
5951:
5948:
5947:
5945:
5944:
5939:
5934:
5929:
5924:
5919:
5913:
5910:
5909:
5906:
5899:
5898:
5895:
5894:
5892:
5891:
5886:
5881:
5876:
5871:
5865:
5862:
5861:
5858:
5851:
5850:
5847:
5846:
5844:
5843:
5838:
5833:
5828:
5823:
5818:
5813:
5808:
5802:
5799:
5798:
5792:
5785:
5784:
5781:
5780:
5778:
5777:
5772:
5767:
5762:
5757:
5751:
5748:
5747:
5744:
5737:
5736:
5733:
5732:
5730:
5729:
5724:
5719:
5714:
5709:
5704:
5699:
5693:
5690:
5689:
5682:
5675:
5674:
5671:
5670:
5668:
5667:
5662:
5657:
5652:
5647:
5642:
5637:
5632:
5627:
5622:
5617:
5612:
5607:
5602:
5596:
5593:
5592:
5586:
5579:
5578:
5572:
5570:
5569:
5562:
5555:
5547:
5538:
5537:
5535:
5534:
5523:
5520:
5519:
5517:
5516:
5511:
5506:
5501:
5496:
5491:
5485:
5483:
5477:
5476:
5474:
5473:
5468:
5466:Fourier series
5463:
5458:
5453:
5451:Puiseux series
5448:
5446:Laurent series
5443:
5438:
5433:
5427:
5425:
5421:
5420:
5417:
5416:
5414:
5413:
5408:
5403:
5398:
5393:
5388:
5383:
5378:
5373:
5368:
5362:
5360:
5356:
5355:
5353:
5352:
5347:
5342:
5337:
5331:
5329:
5322:
5318:
5317:
5314:
5313:
5311:
5310:
5305:
5300:
5294:
5292:
5288:
5287:
5285:
5284:
5279:
5274:
5269:
5263:
5261:
5254:
5250:
5249:
5247:
5246:
5241:
5236:
5230:
5228:
5224:
5223:
5216:
5214:
5211:
5210:
5208:
5207:
5206:
5205:
5195:
5190:
5185:
5180:
5175:
5170:
5165:
5160:
5155:
5149:
5147:
5136:
5135:
5133:
5132:
5127:
5122:
5117:
5112:
5107:
5102:
5097:
5092:
5086:
5084:
5077:
5071:
5070:
5061:
5059:
5058:
5051:
5044:
5036:
5028:
5027:
5019:Huffman coding
5011:
4992:
4985:
4965:
4947:
4921:
4899:
4885:
4866:
4839:
4827:
4824:
4821:
4818:
4813:
4809:
4805:
4801:
4781:
4778:
4775:
4772:
4769:
4764:
4760:
4756:
4752:
4736:
4729:
4705:
4698:
4679:
4678:
4676:
4673:
4672:
4671:
4666:
4664:Power of three
4661:
4656:
4651:
4644:
4641:
4629:
4626:
4609:
4606:
4601:
4597:
4593:
4588:
4584:
4580:
4577:
4574:
4571:
4566:
4562:
4558:
4553:
4549:
4545:
4542:
4537:
4534:
4530:
4526:
4521:
4518:
4514:
4487:
4484:
4480:
4476:
4471:
4468:
4464:
4429:
4425:
4419:
4415:
4411:
4408:
4403:
4399:
4393:
4389:
4385:
4382:
4377:
4373:
4369:
4364:
4360:
4281:
4280:
4269:
4263:
4257:
4251:
4245:
4242:
4237:
4233:
4187:
4184:
4179:
4175:
4163:
4162:
4149:
4145:
4141:
4138:
4135:
4130:
4126:
4122:
4117:
4113:
4109:
4106:
4080:
4069:
4068:
4057:
4054:
4049:
4045:
4041:
4036:
4033:
4030:
4026:
4022:
4019:
4016:
4011:
4007:
4003:
3998:
3994:
3990:
3985:
3981:
3977:
3972:
3968:
3962:
3959:
3956:
3951:
3948:
3945:
3941:
3915:
3911:
3907:
3904:
3884:
3862:
3855:
3850:
3847:
3842:
3833:
3829:
3805:cross-polytope
3775:The number of
3664:
3661:
3636:
3632:
3628:
3625:
3620:
3616:
3612:
3608:
3569:
3566:
3561:
3558:
3555:
3552:
3546:
3543:
3540:
3535:
3532:
3529:
3504:
3500:
3493:
3490:
3484:
3481:
3476:
3472:
3423:sixteenth note
3394:
3391:
3390:
3389:
3382:
3375:
3369:
3362:
3356:
3349:
3338:
3331:
3320:
3314:
3300:
3297:
3286:
3280:
3267:
3261:
3246:
3240:
3227:
3200:
3187:
3164:
3142:IPv6 addresses
3138:
3135:
3128:
3125:
3106:
3103:
3084:
3081:
3068:
3065:
3062:Tower of Hanoi
3058:
3051:
3048:IPv6 addresses
3044:
3029:
3014:
2983:
2980:
2977:
2974:
2971:
2956:
2953:
2946:
2943:
2936:
2933:
2918:
2915:
2900:
2897:
2888:The number of
2886:
2867:
2852:
2837:
2816:
2786:
2785:
2782:
2760:
2759:
2756:
2737:
2734:
2727:
2704:
2689:
2688:2 = 16,777,216
2686:
2667:
2664:
2659:The number of
2657:
2626:
2606:Main article:
2604:
2603:
2600:
2593:
2590:
2579:
2576:
2557:
2554:
2527:
2524:
2513:
2508:
2505:
2468:
2465:
2457:
2456:
2445:
2442:
2434:
2430:
2426:
2422:
2417:
2409:
2405:
2401:
2397:
2392:
2384:
2380:
2376:
2372:
2367:
2359:
2355:
2347:
2343:
2338:
2333:
2326:
2321:
2318:
2315:
2311:
2278:
2274:
2245:
2241:
2236:
2209:
2206:
2173:
2170:
2152:
2151:
2148:
2113:
2110:
2106:
2105:
2102:
2085:72...0,
2067:
2064:
2060:
2059:
2056:
2019:
2016:
2012:
2011:
2008:
1971:
1968:
1964:
1963:
1960:
1923:
1920:
1916:
1915:
1912:
1875:
1872:
1868:
1867:
1864:
1827:
1824:
1820:
1819:
1816:
1779:
1776:
1772:
1771:
1768:
1751:87...8,
1733:
1730:
1726:
1725:
1722:
1687:
1684:
1680:
1679:
1676:
1659:02...1,
1641:
1638:
1634:
1633:
1630:
1595:
1592:
1588:
1587:
1584:
1557:
1554:
1550:
1549:
1546:
1531:
1528:
1524:
1523:
1520:
1517:
1514:
1510:
1509:
1506:
1501:
1498:
1494:
1493:
1490:
1485:
1482:
1478:
1477:
1474:
1469:
1466:
1462:
1461:
1458:
1453:
1450:
1446:
1445:
1442:
1437:
1434:
1430:
1429:
1426:
1410:
1405:
1383:
1380:
1376:IEEE 1541-2002
1366:
1365:
1362:
1359:
1356:
1353:
1349:
1348:
1345:
1342:
1339:
1336:
1332:
1331:
1328:
1325:
1322:
1319:
1315:
1314:
1311:
1308:
1305:
1302:
1298:
1297:
1294:
1291:
1288:
1285:
1281:
1280:
1277:
1274:
1271:
1268:
1264:
1263:
1260:
1257:
1254:
1251:
1247:
1246:
1243:
1240:
1237:
1234:
1230:
1229:
1226:
1223:
1220:
1217:
1213:
1212:
1209:
1206:
1203:
1200:
1196:
1195:
1192:
1189:
1186:
1183:
1158:
1157:Powers of 1024
1155:
1122:
1119:
1116:
1115:
1112:
1109:
1106:
1103:
1102:2,147,483,648
1100:
1097:
1092:
1088:
1087:
1084:
1081:
1078:
1075:
1074:1,073,741,824
1072:
1069:
1064:
1060:
1059:
1056:
1053:
1050:
1047:
1044:
1041:
1036:
1032:
1031:
1028:
1025:
1022:
1019:
1016:
1013:
1008:
1004:
1003:
1000:
997:
994:
991:
988:
985:
980:
976:
975:
972:
969:
966:
963:
960:
957:
952:
948:
947:
944:
941:
938:
935:
932:
929:
924:
920:
919:
916:
913:
910:
907:
904:
901:
896:
892:
891:
888:
885:
882:
879:
876:
873:
868:
864:
863:
860:
857:
854:
851:
848:
845:
840:
836:
835:
832:
829:
826:
823:
820:
817:
812:
808:
807:
804:
801:
798:
795:
792:
789:
784:
780:
779:
776:
773:
770:
767:
764:
761:
756:
752:
751:
748:
745:
742:
739:
736:
733:
728:
724:
723:
720:
717:
716:8,589,934,592
714:
711:
708:
705:
700:
696:
695:
692:
689:
684:
681:
676:
673:
668:
664:
663:
658:
653:
651:
646:
641:
639:
634:
629:
627:
622:
598:
595:
557:is to 16. Now
549:, or 31 is to
525:perfect number
494:
487:
483:polite numbers
455:Mersenne prime
446:
443:
337:
326:
296:
293:
272:
269:
169:
168:
65:exponentiation
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
7894:
7883:
7880:
7878:
7875:
7873:
7870:
7868:
7865:
7864:
7862:
7847:
7844:
7842:
7839:
7838:
7835:
7829:
7826:
7824:
7821:
7819:
7816:
7814:
7811:
7809:
7806:
7804:
7801:
7799:
7796:
7794:
7791:
7789:
7786:
7784:
7781:
7779:
7778:Infinitesimal
7776:
7774:
7771:
7769:
7766:
7764:
7761:
7760:
7758:
7747:
7737:
7734:
7732:
7729:
7727:
7724:
7720:
7717:
7715:
7712:
7711:
7710:
7707:
7706:
7704:
7700:
7694:
7691:
7689:
7686:
7684:
7681:
7679:
7676:
7675:
7673:
7669:
7666:
7660:
7654:
7651:
7649:
7648:Rayo's number
7646:
7644:
7641:
7639:
7636:
7634:
7631:
7629:
7626:
7624:
7621:
7619:
7616:
7614:
7611:
7609:
7606:
7604:
7601:
7599:
7596:
7594:
7591:
7589:
7586:
7584:
7581:
7579:
7576:
7574:
7571:
7569:
7566:
7564:
7561:
7559:
7556:
7554:
7551:
7549:
7546:
7544:
7541:
7539:
7536:
7534:
7531:
7529:
7526:
7525:
7523:
7513:
7509:
7508:Large numbers
7502:
7497:
7495:
7490:
7488:
7483:
7482:
7479:
7467:
7463:
7459:
7458:
7455:
7445:
7442:
7441:
7438:
7433:
7428:
7424:
7414:
7411:
7409:
7406:
7405:
7402:
7397:
7392:
7388:
7378:
7375:
7373:
7370:
7369:
7366:
7361:
7356:
7352:
7342:
7339:
7337:
7334:
7333:
7330:
7326:
7320:
7316:
7306:
7303:
7301:
7298:
7296:
7293:
7292:
7289:
7285:
7280:
7276:
7262:
7259:
7258:
7256:
7252:
7246:
7243:
7241:
7238:
7236:
7235:Polydivisible
7233:
7231:
7228:
7226:
7223:
7221:
7218:
7216:
7213:
7212:
7210:
7206:
7200:
7197:
7195:
7192:
7190:
7187:
7185:
7182:
7180:
7177:
7176:
7174:
7171:
7166:
7160:
7157:
7155:
7152:
7150:
7147:
7145:
7142:
7140:
7137:
7135:
7132:
7130:
7127:
7126:
7124:
7121:
7117:
7109:
7106:
7105:
7104:
7101:
7100:
7098:
7095:
7091:
7079:
7076:
7075:
7074:
7071:
7069:
7066:
7064:
7061:
7059:
7056:
7054:
7051:
7049:
7046:
7044:
7041:
7039:
7036:
7034:
7031:
7030:
7028:
7024:
7018:
7015:
7014:
7012:
7008:
7002:
6999:
6997:
6994:
6993:
6991:
6989:Digit product
6987:
6981:
6978:
6976:
6973:
6971:
6968:
6966:
6963:
6962:
6960:
6958:
6954:
6946:
6943:
6941:
6938:
6937:
6936:
6933:
6932:
6930:
6928:
6923:
6919:
6915:
6910:
6905:
6901:
6891:
6888:
6886:
6883:
6881:
6878:
6876:
6873:
6871:
6868:
6866:
6863:
6861:
6858:
6856:
6853:
6851:
6848:
6846:
6843:
6841:
6838:
6836:
6833:
6831:
6828:
6826:
6825:Erdős–Nicolas
6823:
6821:
6818:
6816:
6813:
6812:
6809:
6804:
6800:
6794:
6790:
6776:
6773:
6771:
6768:
6767:
6765:
6763:
6759:
6753:
6750:
6748:
6745:
6743:
6740:
6738:
6735:
6734:
6732:
6730:
6726:
6720:
6717:
6715:
6712:
6710:
6707:
6705:
6702:
6700:
6697:
6695:
6692:
6691:
6689:
6687:
6683:
6677:
6674:
6672:
6669:
6668:
6666:
6664:
6660:
6654:
6651:
6649:
6646:
6644:
6643:Superabundant
6641:
6639:
6636:
6634:
6631:
6629:
6626:
6624:
6621:
6619:
6616:
6614:
6611:
6609:
6606:
6604:
6601:
6599:
6596:
6594:
6591:
6589:
6586:
6584:
6581:
6579:
6576:
6574:
6571:
6569:
6566:
6564:
6561:
6559:
6556:
6554:
6551:
6549:
6546:
6545:
6543:
6541:
6537:
6533:
6529:
6525:
6520:
6516:
6506:
6503:
6501:
6498:
6496:
6493:
6491:
6488:
6486:
6483:
6481:
6478:
6476:
6473:
6471:
6468:
6466:
6463:
6461:
6458:
6456:
6453:
6451:
6448:
6447:
6444:
6440:
6435:
6431:
6421:
6418:
6416:
6413:
6411:
6408:
6406:
6403:
6402:
6399:
6395:
6390:
6386:
6376:
6373:
6371:
6368:
6366:
6363:
6361:
6358:
6356:
6353:
6351:
6348:
6346:
6343:
6341:
6338:
6336:
6333:
6331:
6328:
6326:
6323:
6321:
6318:
6316:
6313:
6311:
6308:
6306:
6303:
6301:
6298:
6296:
6293:
6291:
6288:
6286:
6283:
6281:
6278:
6277:
6274:
6267:
6263:
6245:
6242:
6240:
6237:
6235:
6232:
6231:
6229:
6225:
6222:
6220:
6219:4-dimensional
6216:
6206:
6203:
6202:
6200:
6198:
6194:
6188:
6185:
6183:
6180:
6178:
6175:
6173:
6170:
6168:
6165:
6163:
6160:
6159:
6157:
6155:
6151:
6145:
6142:
6140:
6137:
6135:
6132:
6130:
6129:Centered cube
6127:
6125:
6122:
6121:
6119:
6117:
6113:
6110:
6108:
6107:3-dimensional
6104:
6094:
6091:
6089:
6086:
6084:
6081:
6079:
6076:
6074:
6071:
6069:
6066:
6064:
6061:
6059:
6056:
6054:
6051:
6049:
6046:
6045:
6043:
6041:
6037:
6031:
6028:
6026:
6023:
6021:
6018:
6016:
6013:
6011:
6008:
6006:
6003:
6001:
5998:
5996:
5993:
5991:
5988:
5987:
5985:
5983:
5979:
5976:
5974:
5973:2-dimensional
5970:
5966:
5962:
5957:
5953:
5943:
5940:
5938:
5935:
5933:
5930:
5928:
5925:
5923:
5920:
5918:
5917:Nonhypotenuse
5915:
5914:
5911:
5904:
5900:
5890:
5887:
5885:
5882:
5880:
5877:
5875:
5872:
5870:
5867:
5866:
5863:
5856:
5852:
5842:
5839:
5837:
5834:
5832:
5829:
5827:
5824:
5822:
5819:
5817:
5814:
5812:
5809:
5807:
5804:
5803:
5800:
5795:
5790:
5786:
5776:
5773:
5771:
5768:
5766:
5763:
5761:
5758:
5756:
5753:
5752:
5749:
5742:
5738:
5728:
5725:
5723:
5720:
5718:
5715:
5713:
5710:
5708:
5705:
5703:
5700:
5698:
5695:
5694:
5691:
5686:
5680:
5676:
5666:
5663:
5661:
5658:
5656:
5655:Perfect power
5653:
5651:
5648:
5646:
5645:Seventh power
5643:
5641:
5638:
5636:
5633:
5631:
5628:
5626:
5623:
5621:
5618:
5616:
5613:
5611:
5608:
5606:
5603:
5601:
5598:
5597:
5594:
5589:
5584:
5580:
5576:
5568:
5563:
5561:
5556:
5554:
5549:
5548:
5545:
5533:
5525:
5524:
5521:
5515:
5512:
5510:
5507:
5505:
5502:
5500:
5497:
5495:
5492:
5490:
5487:
5486:
5484:
5482:
5478:
5472:
5469:
5467:
5464:
5462:
5459:
5457:
5454:
5452:
5449:
5447:
5444:
5442:
5439:
5437:
5434:
5432:
5431:Taylor series
5429:
5428:
5426:
5422:
5412:
5409:
5407:
5404:
5402:
5399:
5397:
5394:
5392:
5389:
5387:
5384:
5382:
5379:
5377:
5374:
5372:
5369:
5367:
5364:
5363:
5361:
5357:
5351:
5348:
5346:
5343:
5341:
5338:
5336:
5333:
5332:
5330:
5326:
5323:
5319:
5309:
5306:
5304:
5301:
5299:
5296:
5295:
5293:
5289:
5283:
5280:
5278:
5275:
5273:
5270:
5268:
5265:
5264:
5262:
5258:
5255:
5251:
5245:
5242:
5240:
5237:
5235:
5232:
5231:
5229:
5225:
5220:
5204:
5201:
5200:
5199:
5196:
5194:
5191:
5189:
5186:
5184:
5181:
5179:
5176:
5174:
5171:
5169:
5166:
5164:
5161:
5159:
5156:
5154:
5151:
5150:
5148:
5144:
5137:
5131:
5128:
5126:
5123:
5121:
5120:Powers of two
5118:
5116:
5113:
5111:
5108:
5106:
5105:Square number
5103:
5101:
5098:
5096:
5093:
5091:
5088:
5087:
5085:
5081:
5078:
5076:
5072:
5068:
5064:
5057:
5052:
5050:
5045:
5043:
5038:
5037:
5034:
5024:
5020:
5015:
5012:
5007:
5003:
4996:
4993:
4988:
4982:
4978:
4977:
4969:
4966:
4961:
4957:
4951:
4948:
4936:
4932:
4925:
4922:
4917:
4913:
4909:
4903:
4900:
4894:
4892:
4890:
4886:
4881:
4877:
4873:
4869:
4867:0-387-20860-7
4863:
4859:
4855:
4854:
4849:
4843:
4840:
4825:
4822:
4819:
4816:
4811:
4807:
4803:
4799:
4779:
4776:
4773:
4770:
4767:
4762:
4758:
4754:
4750:
4740:
4737:
4732:
4730:0-19-851494-8
4726:
4722:
4718:
4717:
4709:
4706:
4701:
4699:0-07-037990-4
4695:
4691:
4684:
4681:
4674:
4670:
4667:
4665:
4662:
4660:
4657:
4655:
4652:
4650:
4647:
4646:
4642:
4640:
4638:
4634:
4633:Huffman codes
4627:
4625:
4623:
4604:
4599:
4595:
4591:
4586:
4582:
4575:
4569:
4564:
4560:
4556:
4551:
4547:
4540:
4535:
4532:
4528:
4524:
4519:
4516:
4512:
4503:
4485:
4482:
4478:
4474:
4469:
4466:
4462:
4453:
4449:
4445:
4427:
4417:
4413:
4406:
4401:
4391:
4387:
4380:
4375:
4371:
4367:
4362:
4358:
4349:
4345:
4341:
4337:
4333:
4329:
4325:
4321:
4317:
4314:is odd, then
4313:
4309:
4305:
4301:
4297:
4293:
4288:
4286:
4267:
4261:
4255:
4249:
4243:
4240:
4235:
4231:
4223:
4222:
4221:
4219:
4214:
4212:
4208:
4204:
4199:
4185:
4182:
4177:
4173:
4147:
4143:
4139:
4136:
4133:
4128:
4124:
4120:
4115:
4111:
4107:
4104:
4097:
4096:
4095:
4092:
4078:
4055:
4052:
4047:
4043:
4039:
4034:
4031:
4028:
4024:
4020:
4017:
4014:
4009:
4005:
4001:
3996:
3992:
3988:
3983:
3979:
3975:
3970:
3966:
3960:
3957:
3954:
3949:
3946:
3943:
3939:
3931:
3930:
3929:
3913:
3909:
3905:
3902:
3882:
3873:
3860:
3848:
3845:
3831:
3827:
3806:
3803:-dimensional
3799:-faces of an
3796:
3786:
3783:-dimensional
3778:
3773:
3770:
3762:
3750:
3745:
3741:
3736:
3734:
3729:
3707:
3695:
3681:
3674:
3669:
3662:
3660:
3658:
3654:
3650:
3634:
3630:
3626:
3623:
3618:
3614:
3610:
3606:
3597:
3593:
3592:perfect fifth
3589:
3585:
3567:
3564:
3559:
3556:
3553:
3550:
3544:
3541:
3538:
3533:
3530:
3527:
3502:
3491:
3488:
3479:
3474:
3470:
3462:
3457:
3455:
3451:
3447:
3442:
3440:
3436:
3432:
3428:
3424:
3420:
3416:
3412:
3408:
3404:
3400:
3392:
3387:
3383:
3376:
3374:
3370:
3363:
3361:
3357:
3350:
3347:
3343:
3339:
3332:
3329:
3325:
3321:
3315:
3312:
3307:
3301:
3298:
3295:
3291:
3287:
3281:
3278:
3273:
3268:
3262:
3259:
3255:
3251:
3247:
3241:
3238:
3233:
3228:
3201:
3198:
3193:
3188:
3165:
3162:
3151:
3147:
3143:
3139:
3136:
3133:
3129:
3126:
3123:
3119:
3115:
3111:
3107:
3104:
3101:
3097:
3093:
3089:
3085:
3082:
3079:
3074:
3069:
3066:
3063:
3059:
3056:
3052:
3049:
3045:
3042:
3038:
3034:
3030:
3027:
3023:
3019:
3015:
3012:
3008:
3004:
3000:
2996:
2992:
2988:
2984:
2981:
2978:
2975:
2972:
2969:
2965:
2961:
2957:
2954:
2951:
2947:
2944:
2941:
2937:
2934:
2931:
2927:
2923:
2919:
2916:
2913:
2909:
2905:
2901:
2898:
2895:
2891:
2887:
2884:
2881:(but not for
2880:
2876:
2872:
2868:
2865:
2861:
2857:
2853:
2850:
2838:
2835:
2831:
2827:
2822:
2817:
2814:
2810:
2806:
2802:
2798:
2794:
2793:
2791:
2790:4,294,967,295
2783:
2780:
2776:
2772:
2768:
2767:
2765:
2764:2,147,483,647
2757:
2754:
2750:
2746:
2742:
2738:
2735:
2732:
2728:
2709:
2705:
2702:
2698:
2694:
2690:
2687:
2684:
2680:
2676:
2672:
2668:
2666:2 = 1,048,576
2665:
2662:
2658:
2655:
2651:
2647:
2643:
2639:
2635:
2631:
2630:short integer
2627:
2624:
2620:
2616:
2612:
2611:
2609:
2601:
2598:
2594:
2591:
2588:
2584:
2581:The hardware
2580:
2577:
2574:
2570:
2566:
2562:
2558:
2555:
2552:
2548:
2544:
2541:. (The term
2540:
2536:
2532:
2528:
2525:
2522:
2518:
2514:
2511:
2510:
2506:
2504:
2502:
2482:
2478:
2474:
2466:
2464:
2462:
2443:
2440:
2432:
2428:
2424:
2420:
2415:
2407:
2403:
2399:
2395:
2390:
2382:
2378:
2374:
2370:
2365:
2357:
2353:
2345:
2341:
2336:
2331:
2319:
2316:
2313:
2309:
2301:
2300:
2299:
2298:
2294:
2276:
2272:
2263:
2243:
2239:
2234:
2224:
2222:
2220:
2215:
2207:
2205:
2203:
2197:
2188:
2180:
2171:
2169:
2167:
2163:
2159:
2158:Fermat number
2149:
2131:6...1,
2114:
2111:
2108:
2107:
2103:
2068:
2065:
2062:
2061:
2057:
2020:
2017:
2014:
2013:
2009:
1972:
1969:
1966:
1965:
1961:
1924:
1921:
1918:
1917:
1913:
1876:
1873:
1870:
1869:
1865:
1828:
1825:
1822:
1821:
1817:
1780:
1777:
1774:
1773:
1769:
1734:
1731:
1728:
1727:
1723:
1705:5...6,
1688:
1685:
1682:
1681:
1677:
1642:
1639:
1636:
1635:
1631:
1613:9...4,
1596:
1593:
1590:
1589:
1585:
1558:
1555:
1552:
1551:
1547:
1532:
1529:
1526:
1525:
1521:
1519:4,294,967,296
1518:
1515:
1512:
1511:
1507:
1505:
1502:
1499:
1496:
1495:
1491:
1489:
1486:
1483:
1480:
1479:
1475:
1473:
1470:
1467:
1464:
1463:
1459:
1457:
1454:
1451:
1448:
1447:
1443:
1441:
1438:
1435:
1432:
1431:
1427:
1424:
1419:
1411:
1406:
1401:
1400:
1395:
1393:
1381:
1379:
1377:
1373:
1360:
1354:
1351:
1350:
1343:
1337:
1334:
1333:
1326:
1320:
1317:
1316:
1309:
1303:
1300:
1299:
1292:
1286:
1283:
1282:
1275:
1269:
1266:
1265:
1258:
1252:
1249:
1248:
1241:
1235:
1232:
1231:
1224:
1218:
1215:
1214:
1207:
1201:
1198:
1197:
1190:
1184:
1181:
1180:
1175:
1172:
1170:
1165:
1156:
1154:
1152:
1146:
1137:
1129:
1120:
1110:
1104:
1098:
1096:
1090:
1089:
1082:
1076:
1070:
1068:
1062:
1061:
1054:
1048:
1042:
1040:
1034:
1033:
1026:
1020:
1014:
1012:
1006:
1005:
998:
992:
986:
984:
978:
977:
970:
964:
958:
956:
950:
949:
942:
936:
930:
928:
922:
921:
914:
908:
902:
900:
894:
893:
886:
880:
874:
872:
866:
865:
858:
852:
846:
844:
838:
837:
830:
824:
818:
816:
810:
809:
802:
796:
790:
788:
782:
781:
774:
768:
762:
760:
754:
753:
746:
740:
734:
732:
726:
725:
718:
712:
706:
704:
698:
697:
690:
688:
687:4,294,967,296
682:
680:
674:
672:
666:
665:
659:
654:
647:
642:
635:
630:
623:
618:
617:
612:
610:
605:
596:
594:
577:implies that
576:
543:
534:
528:
526:
523:th term is a
514:
513:
508:
507:number theory
504:
500:
492:
486:
484:
480:
476:
472:
468:
464:
460:
456:
452:
444:
442:
439:480 = 32 × 15
435:640 = 32 × 20
430:
428:
423:
421:
417:
413:
409:
405:
401:
397:
393:
389:
385:
380:
378:
374:
370:
369:
360:
356:
352:
348:
344:
322:
314:
310:
303:, written as
294:
292:
290:
286:
282:
278:
270:
268:
266:
262:
186:
174:
166:
161:
156:
152:
148:
144:
140:
136:
132:
128:
124:
120:
117:
116:
115:
105:
89:
84:
82:
74:
70:
66:
62:
50:
43:
42:Dienes blocks
38:
33:
19:
18:Powers of two
7813:Power of two
7812:
7803:Number names
7538:Ten thousand
7199:Transposable
7063:Narcissistic
6970:Digital root
6890:Super-Poulet
6850:Jordan–Pólya
6799:prime factor
6704:Noncototient
6671:Almost prime
6653:Superperfect
6628:Refactorable
6623:Quasiperfect
6598:Hyperperfect
6439:Pseudoprimes
6410:Wall–Sun–Sun
6345:Ordered Bell
6315:Fuss–Catalan
6227:non-centered
6177:Dodecahedral
6154:non-centered
6040:non-centered
5942:Wolstenholme
5687:× 2 ± 1
5684:
5683:Of the form
5650:Eighth power
5630:Fourth power
5604:
5436:Power series
5178:Lucas number
5130:Powers of 10
5119:
5110:Cubic number
5022:
5014:
4995:
4975:
4968:
4959:
4950:
4939:. Retrieved
4924:
4916:the original
4911:
4902:
4852:
4842:
4739:
4715:
4708:
4689:
4683:
4631:
4621:
4501:
4447:
4443:
4347:
4343:
4339:
4335:
4331:
4327:
4323:
4319:
4315:
4311:
4307:
4299:
4295:
4289:
4282:
4215:
4200:
4164:
4093:
4070:
3874:
3794:
3774:
3768:
3760:
3748:
3737:
3730:
3696:is equal to
3687:
3458:
3443:
3434:
3421:(1/8) and a
3415:quarter note
3396:
3250:IP addresses
3153:
3036:
3032:
2970:or exbibyte.
2932:or pebibyte.
2914:or tebibyte.
2871:IP addresses
2856:long integer
2770:
2649:
2645:
2596:
2480:
2476:
2470:
2458:
2226:The numbers
2225:
2217:
2211:
2195:
2175:
2155:
2039:...1,
1991:...2,
1943:...7,
1895:...2,
1847:...1,
1799:...0,
1385:
1369:
1173:
1160:
1144:
1124:
1046:536,870,912
1018:268,435,456
990:134,217,728
600:
545:is equal to
541:
529:
511:
496:
490:
477:is called a
467:Fermat prime
451:prime number
448:
431:
424:
415:
403:
399:
395:
387:
381:
366:
298:
274:
260:
170:
88:non-negative
85:
67:with number
49:power of two
48:
46:
7823:Power of 10
7763:Busy beaver
7568:Quintillion
7563:Quadrillion
7220:Extravagant
7215:Equidigital
7170:permutation
7129:Palindromic
7103:Automorphic
7001:Sum-product
6980:Sum-product
6935:Persistence
6830:Erdős–Woods
6752:Untouchable
6633:Semiperfect
6583:Hemiperfect
6244:Tesseractic
6182:Icosahedral
6162:Tetrahedral
6093:Dodecagonal
5794:Recursively
5665:Prime power
5640:Sixth power
5635:Fifth power
5615:Power of 10
5573:Classes of
5303:Conditional
5291:Convergence
5282:Telescoping
5267:Alternating
5183:Pell number
4669:Power of 10
4620:, even if
4304:irreducible
3740:cardinality
3706:cardinality
3446:frequencies
3439:denominator
3419:eighth note
3403:note values
3224:052,
3222:942,
3220:857,
3218:651,
3216:843,
3214:865,
3212:615,
3210:234,
3208:730,
3206:591,
3204:070,
3184:576,
3182:020,
3180:156,
3178:783,
3176:726,
3174:426,
3172:658,
3170:553,
3168:518,
3132:conjectured
3013:processors.
2885:addresses).
2815:processors.
2625:processors.
2585:size of an
2193:, which is
2145:773,
2143:185,
2141:226,
2139:528,
2137:364,
2135:814,
2133:369,
2129:659,
2127:612,
2125:077,
2123:100,
2121:783,
2119:056,
2117:637,
2099:300,
2097:298,
2095:934,
2093:349,
2091:605,
2089:862,
2087:753,
2083:195,
2081:736,
2079:604,
2077:857,
2075:174,
2073:257,
2071:113,
2053:173,
2051:934,
2049:570,
2047:318,
2045:812,
2043:665,
2041:850,
2037:060,
2035:166,
2033:039,
2031:063,
2029:036,
2027:182,
2025:132,
2023:014,
2005:156,
2003:719,
2001:905,
1999:895,
1997:587,
1995:445,
1993:339,
1989:072,
1987:979,
1985:464,
1983:846,
1981:406,
1979:930,
1977:529,
1975:003,
1957:377,
1955:712,
1953:633,
1951:104,
1949:668,
1947:122,
1945:541,
1941:553,
1939:001,
1937:789,
1935:954,
1933:044,
1931:031,
1929:461,
1927:415,
1909:066,
1907:964,
1905:669,
1903:290,
1901:027,
1899:447,
1897:460,
1893:759,
1891:085,
1889:765,
1887:231,
1885:357,
1883:495,
1881:731,
1879:189,
1861:792,
1859:715,
1857:475,
1855:665,
1853:505,
1851:186,
1849:997,
1845:984,
1843:462,
1841:929,
1839:415,
1837:619,
1835:135,
1833:748,
1831:090,
1813:190,
1811:154,
1809:403,
1807:340,
1805:708,
1803:804,
1801:243,
1797:752,
1795:691,
1793:506,
1791:152,
1789:413,
1787:881,
1785:388,
1783:044,
1765:230,
1763:596,
1761:059,
1759:611,
1757:853,
1755:555,
1753:193,
1749:714,
1747:300,
1745:007,
1743:311,
1741:071,
1739:006,
1737:317,
1719:137,
1717:224,
1715:624,
1713:329,
1711:356,
1709:835,
1707:304,
1703:930,
1701:772,
1699:590,
1697:231,
1695:486,
1693:313,
1691:769,
1673:084,
1671:006,
1669:649,
1667:433,
1665:946,
1663:569,
1661:946,
1657:574,
1655:099,
1653:597,
1651:942,
1649:929,
1647:807,
1645:407,
1627:639,
1625:129,
1623:913,
1621:007,
1619:584,
1617:457,
1615:039,
1611:570,
1609:423,
1607:195,
1605:316,
1603:237,
1601:089,
1599:792,
1581:211,
1579:768,
1577:431,
1575:607,
1573:374,
1571:463,
1569:463,
1567:938,
1565:920,
1563:366,
1561:282,
1543:551,
1541:709,
1539:073,
1537:744,
1535:446,
1142:, which is
1121:Last digits
962:67,108,864
934:33,554,432
906:16,777,216
585:be 4, then
475:denominator
427:disk drives
377:kill screen
363:2 − 1 = 255
359:8 bits long
357:, which is
313:binary word
285:power of 10
7882:2 (number)
7861:Categories
7828:Sagan Unit
7662:Expression
7613:Googolplex
7578:Septillion
7573:Sextillion
7519:numerical
7432:Graphemics
7305:Pernicious
7159:Undulating
7134:Pandigital
7108:Trimorphic
6709:Nontotient
6558:Arithmetic
6172:Octahedral
6073:Heptagonal
6063:Pentagonal
6048:Triangular
5889:Sierpiński
5811:Jacobsthal
5610:Power of 3
5605:Power of 2
5328:Convergent
5272:Convergent
4941:2013-05-29
4876:1058.11001
4675:References
4292:polynomial
4290:As a real
3815:-faces an
3752:is always
3417:(1/4), an
3407:whole note
3226:864
3186:256
2995:doubleword
2805:doubleword
2788:See also:
2762:See also:
2714:) to 255 (
2602:2 = 65,536
2592:2 = 32,768
2475:to have a
2473:data types
2147:056
2101:416
2055:696
2007:736
1959:856
1911:816
1863:896
1815:336
1767:656
1721:216
1675:096
1629:936
1583:456
1545:616
1415:(sequence
1205:1 024
1161:(sequence
878:8,388,608
850:4,194,304
822:2,097,152
794:1,048,576
601:(sequence
351:video game
315:of length
106:by itself
104:multiplied
7719:Pentation
7714:Tetration
7702:Operators
7671:Notations
7593:Decillion
7588:Nonillion
7583:Octillion
7515:Examples
7189:Parasitic
7038:Factorion
6965:Digit sum
6957:Digit sum
6775:Fortunate
6762:Primorial
6676:Semiprime
6613:Practical
6578:Descartes
6573:Deficient
6563:Betrothed
6405:Wieferich
6234:Pentatope
6197:pyramidal
6088:Decagonal
6083:Nonagonal
6078:Octagonal
6068:Hexagonal
5927:Practical
5874:Congruent
5806:Fibonacci
5770:Loeschian
5359:Divergent
5277:Divergent
5139:Advanced
5115:Factorial
5063:Sequences
4823:≈
4817:
4774:≈
4768:
4592:−
4576:⋅
4330:, and if
4183:−
4137:⋯
4053:−
4032:−
4018:⋯
3958:−
3940:∑
3785:hypercube
3746:of a set
3744:power set
3624:≈
3584:semitones
3560:≈
3557:…
3542:
3531:
3480:≈
3435:beat unit
3413:(1/2), a
3411:half note
3328:key space
3294:key space
3118:yottabyte
3096:zettabyte
2775:Unix time
2747:= 1
2697:truecolor
2677:= 1
2587:Intel x86
2578:2 = 4,096
2567:= 1
2556:2 = 1,024
2521:tetration
2444:⋯
2325:∞
2310:∑
2162:tetration
2156:Also see
493:, Book IX
489:Euclid's
336:111...111
325:000...000
173:fractions
7877:Integers
7751:articles
7749:Related
7653:Infinity
7558:Trillion
7533:Thousand
7261:Friedman
7194:Primeval
7139:Repdigit
7096:-related
7043:Kaprekar
7017:Meertens
6940:Additive
6927:dynamics
6835:Friendly
6747:Sociable
6737:Amicable
6548:Abundant
6528:dynamics
6350:Schröder
6340:Narayana
6310:Eulerian
6300:Delannoy
6295:Dedekind
6116:centered
5982:centered
5869:Amenable
5826:Narayana
5816:Leonardo
5712:Mersenne
5660:Powerful
5600:Achilles
5532:Category
5298:Absolute
5021:, from:
5006:Archived
4935:Archived
4880:archived
4643:See also
4346:, where
3807:is also
3777:vertices
3756:, where
3692:-choose
3450:interval
3425:(1/16).
3377:2 ≈ 1.49
3364:2 ≈ 1.61
3351:2 ≈ 1.19
3333:2 ≈ 1.79
3326:256-bit
3292:192-bit
3166:2 = 324,
3122:yobibyte
3100:zebibyte
3003:quadword
2930:petabyte
2912:terabyte
2841:Cardinal
2753:gibibyte
2749:gigabyte
2683:mebibyte
2679:megabyte
2650:Smallint
2573:kibibyte
2569:kilobyte
2551:kilobyte
2260:form an
2221:2-powers
2150:157,827
2112:524,288
2066:262,144
2018:131,072
766:524,288
738:262,144
710:131,072
512:Elements
491:Elements
471:fraction
291:system.
185:one half
81:exponent
7846:History
7664:methods
7638:SSCG(3)
7633:TREE(3)
7553:Billion
7548:Million
7528:Hundred
7434:related
7398:related
7362:related
7360:Sorting
7245:Vampire
7230:Harshad
7172:related
7144:Repunit
7058:Lychrel
7033:Dudeney
6885:Størmer
6880:Sphenic
6865:Regular
6803:divisor
6742:Perfect
6638:Sublime
6608:Perfect
6335:Motzkin
6290:Catalan
5831:Padovan
5765:Leyland
5760:Idoneal
5755:Hilbert
5727:Woodall
5308:Uniform
4500:(where
3742:of the
3517:, from
3454:octaves
3309:in the
3306:A330024
3275:in the
3272:A137214
3235:in the
3232:A050723
3202:2 = 85,
3195:in the
3192:A035064
3076:in the
3073:A137214
2968:exabyte
2845:Integer
2724:#FFFFFF
2720:#000000
2526:2 = 256
2523:of two.
2214:nimbers
2104:78,914
2058:39,457
2010:19,729
1970:65,536
1428:digits
1421:in the
1418:A001146
1361:≈ 1000
1344:≈ 1000
1167:in the
1164:A140300
607:in the
604:A000079
547:16 × 31
373:Pac-Man
334: (
321:integer
289:decimal
287:in the
257:
245:
241:
229:
225:
213:
209:
197:
163:in the
160:A000079
102:is two
79:as the
71:as the
61:integer
7755:order)
7603:Googol
7300:Odious
7225:Frugal
7179:Cyclic
7168:Digit-
6875:Smooth
6860:Pronic
6820:Cyclic
6797:Other
6770:Euclid
6420:Wilson
6394:Primes
6053:Square
5922:Polite
5884:Riesel
5879:Knödel
5841:Perrin
5722:Thabit
5707:Fermat
5697:Cullen
5620:Square
5588:Powers
5260:Series
5067:series
5025:, 2006
4983:
4931:"Zero"
4874:
4864:
4727:
4696:
4265:
4259:
4253:
4247:
4209:. The
3779:of an
3764:|
3758:|
3554:1.5849
3427:Dotted
3110:yotta-
3088:zetta-
3041:Pascal
3007:16-bit
2999:32-bit
2991:64-bit
2873:under
2849:Pascal
2832:, and
2809:16-bit
2801:32-bit
2771:signed
2731:24-bit
2693:colors
2654:Pascal
2640:, and
2619:16-bit
2608:65,536
2597:signed
2517:square
2481:values
2297:series
2295:, the
2219:Fermat
2196:φ
1962:9,865
1922:32,768
1914:4,933
1874:16,384
1866:2,467
1818:1,234
1504:65,536
1327:≈ 1000
1310:≈ 1000
1293:≈ 1000
1276:≈ 1000
1259:≈ 1000
1242:≈ 1000
1225:≈ 1000
1208:≈ 1000
1191:= 1000
1145:φ
1095:32,768
1067:16,384
679:65,536
533:divide
437:, and
343:signed
98:, and
59:is an
55:where
7841:Names
7643:BH(3)
7521:order
7341:Prime
7336:Lucky
7325:sieve
7254:Other
7240:Smith
7120:Digit
7078:Happy
7053:Keith
7026:Other
6870:Rough
6840:Giuga
6305:Euler
6167:Cubic
5821:Lucas
5717:Proth
5203:array
5083:Basic
4826:29.2.
3590:to a
3148:. In
3130:2 is
3114:bytes
3092:bytes
3037:QWord
3033:Int64
3005:on a
2997:on a
2989:on a
2964:bytes
2926:bytes
2922:peta-
2908:bytes
2904:tera-
2807:on a
2799:on a
2745:bytes
2741:giga-
2675:bytes
2671:mega-
2617:on a
2565:bytes
2561:kilo-
2539:octet
2533:in a
2512:2 = 4
2497:2 − 1
2489:2 − 1
2200:(see
1826:8,192
1778:4,096
1732:2,048
1686:1,024
1149:(see
1039:8,192
1011:4,096
983:2,048
955:1,024
384:octet
332:2 − 1
330:) to
311:in a
114:are:
96:2 = 2
92:2 = 1
7295:Evil
6975:Self
6925:and
6815:Blum
6526:and
6330:Lobb
6285:Cake
6280:Bell
6030:Star
5937:Ulam
5836:Pell
5625:Cube
5143:list
5065:and
4981:ISBN
4862:ISBN
4812:1000
4804:1024
4777:17.1
4763:1000
4755:1024
4725:ISBN
4694:ISBN
4268:664.
4201:The
4071:for
3797:− 1)
3738:The
3459:The
3316:2 =
3311:OEIS
3282:2 =
3277:OEIS
3263:2 =
3254:IPv6
3242:2 =
3237:OEIS
3197:OEIS
3150:CIDR
3120:(or
3116:= 1
3098:(or
3094:= 1
3078:OEIS
3024:and
3022:Java
3018:long
2987:word
2966:= 1
2960:exa-
2928:= 1
2910:= 1
2896:(4).
2883:IPv6
2875:IPv4
2862:and
2826:Java
2797:word
2751:(or
2681:(or
2646:Word
2638:Java
2615:word
2583:page
2571:(or
2543:byte
2535:byte
2531:bits
2495:and
2477:size
2179:base
2177:any
2164:and
2115:259,
1770:617
1724:309
1689:179,
1678:155
1597:115,
1559:340,
1423:OEIS
1374:and
1169:OEIS
1128:base
609:OEIS
569:and
497:The
416:kibi
404:kilo
400:byte
396:kilo
388:byte
355:byte
309:bits
165:OEIS
73:base
7413:Ban
6801:or
6320:Lah
4872:Zbl
4800:log
4771:1.5
4751:log
4302:is
4262:177
4256:744
4250:368
4205:is
3787:is
3708:is
3684:two
3598::
3594:of
3586:in
3539:log
3528:log
3397:In
3324:AES
3290:AES
3035:or
3011:x86
2950:DES
2864:C++
2843:or
2834:SQL
2821:int
2813:x86
2708:RGB
2648:or
2642:SQL
2623:x86
2291:of
2204:).
2109:19
2069:16,
2063:18
2015:17
1967:16
1735:32,
1643:13,
1640:512
1632:78
1594:256
1586:39
1556:128
1548:20
1533:18,
1522:10
1488:256
1390:),
1153:).
927:512
899:256
871:128
553:as
542:p q
463:257
183:is
155:512
151:256
147:128
69:two
7863::
7517:in
4958:.
4933:.
4910:.
4888:^
4878:,
4870:,
4723:.
4721:78
4446:+
4344:mp
4318:+
4298:+
4294:,
4244:70
4236:46
4178:64
4148:63
3772:.
3735:.
3659:.
3619:12
3568:12
3565:19
3503:12
3381:10
3368:10
3355:10
3348:).
3337:10
3159:32
3124:).
3102:).
3026:C#
2894:GF
2830:C#
2828:,
2755:).
2716:FF
2712:00
2685:).
2636:,
2634:C#
2575:).
2553:.)
2503:.
2493:−2
2425:16
2223:.
2168:.
2160:,
2021:4,
1973:2,
1925:1,
1919:15
1877:1,
1871:14
1829:1,
1823:13
1781:1,
1775:12
1729:11
1683:10
1530:64
1516:32
1508:5
1500:16
1492:3
1476:2
1472:16
1460:1
1444:1
1378:.
1171:)
1111:63
1105:47
1099:31
1091:15
1083:62
1077:46
1071:30
1063:14
1055:61
1049:45
1043:29
1035:13
1027:60
1021:44
1015:28
1007:12
999:59
993:43
987:27
979:11
971:58
965:42
959:26
951:10
943:57
937:41
931:25
915:56
909:40
903:24
887:55
881:39
875:23
859:54
853:38
847:22
843:64
831:53
825:37
819:21
815:32
803:52
797:36
791:20
787:16
775:51
769:35
763:19
747:50
741:34
735:18
719:49
713:33
707:17
691:48
683:32
675:16
611:)
459:31
449:A
254:16
243:,
227:,
211:,
179:,
153:,
149:,
145:,
143:64
141:,
139:32
137:,
135:16
133:,
129:,
125:,
121:,
94:,
83:.
47:A
7500:e
7493:t
7486:v
5685:a
5566:e
5559:t
5552:v
5145:)
5141:(
5055:e
5048:t
5041:v
4989:.
4962:.
4944:.
4820:2
4808:/
4780:,
4759:/
4733:.
4702:.
4622:n
4608:)
4605:i
4600:n
4596:b
4587:n
4583:a
4579:(
4573:)
4570:i
4565:n
4561:b
4557:+
4552:n
4548:a
4544:(
4541:=
4536:n
4533:2
4529:b
4525:+
4520:n
4517:2
4513:a
4502:n
4486:n
4483:2
4479:b
4475:+
4470:n
4467:2
4463:a
4448:b
4444:a
4428:m
4424:)
4418:p
4414:b
4410:(
4407:+
4402:m
4398:)
4392:p
4388:a
4384:(
4381:=
4376:n
4372:b
4368:+
4363:n
4359:a
4348:m
4342:=
4340:n
4336:n
4332:n
4328:b
4326:+
4324:a
4320:b
4316:a
4312:n
4308:n
4300:b
4296:a
4241:=
4232:2
4207:1
4186:1
4174:2
4144:2
4140:+
4134:+
4129:2
4125:2
4121:+
4116:1
4112:2
4108:+
4105:1
4079:n
4056:1
4048:n
4044:2
4040:=
4035:1
4029:n
4025:2
4021:+
4015:+
4010:2
4006:2
4002:+
3997:1
3993:2
3989:+
3984:0
3980:2
3976:=
3971:k
3967:2
3961:1
3955:n
3950:0
3947:=
3944:k
3914:0
3910:2
3906:=
3903:1
3883:n
3861:.
3854:)
3849:x
3846:n
3841:(
3832:x
3828:2
3817:n
3813:x
3809:2
3801:n
3795:n
3793:(
3789:2
3781:n
3769:a
3761:a
3754:2
3749:a
3726:n
3722:n
3718:n
3714:n
3710:2
3702:n
3698:2
3690:n
3635:2
3631:/
3627:3
3615:/
3611:7
3607:2
3551:=
3545:2
3534:3
3499:)
3492:2
3489:3
3483:(
3475:7
3471:2
3379:×
3366:×
3353:×
3335:×
3313:)
3279:)
3260:.
3239:)
3199:)
3156:/
3080:)
3064:.
2860:C
2781:.
2703:.
2485:2
2441:+
2433:2
2429:x
2421:1
2416:+
2408:1
2404:x
2400:4
2396:1
2391:+
2383:0
2379:x
2375:2
2371:1
2366:=
2358:i
2354:x
2346:i
2342:2
2337:2
2332:1
2320:0
2317:=
2314:i
2277:i
2273:x
2244:n
2240:2
2235:2
2191:5
2183:2
1637:9
1591:8
1553:7
1527:6
1513:5
1497:4
1484:8
1481:3
1468:4
1465:2
1456:4
1452:2
1449:1
1440:2
1436:1
1433:0
1425:)
1413:2
1408:2
1403:n
1388:2
1355:=
1352:2
1338:=
1335:2
1321:=
1318:2
1304:=
1301:2
1287:=
1284:2
1270:=
1267:2
1253:=
1250:2
1236:=
1233:2
1219:=
1216:2
1202:=
1199:2
1188:1
1185:=
1182:2
1140:5
1132:2
923:9
895:8
867:7
839:6
811:5
783:4
759:8
755:3
731:4
727:2
703:2
699:1
671:1
667:0
661:2
656:n
649:2
644:n
637:2
632:n
625:2
620:n
591:p
587:p
583:q
579:q
571:q
567:q
563:q
559:p
555:p
551:q
537:p
521:n
517:n
338:2
327:2
317:n
305:2
301:n
251:/
248:1
238:8
235:/
232:1
222:4
219:/
216:1
206:2
203:/
200:1
193:n
189:n
181:2
177:n
167:)
131:8
127:4
123:2
119:1
112:n
108:n
100:2
77:n
57:n
53:2
20:)
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