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in 2008 states that all odd integers greater than 3 can be represented as the sum of a prime number and the product of two consecutive positive integers (
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189:, the conjecture has been verified by Corbitt up to 10. A blog post in June of 2019 additionally claimed to have verified the conjecture up to 10.
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For example, the odd integer 47 can be expressed as the sum of a prime and a semiprime in four different ways:
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Agama, Theophilus; Gensel, Berndt (21 March 2021). "A Proof of
Lemoine's Conjecture by Circles of Partition".
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John O. Kiltinen and Peter B. Young, "Goldbach, Lemoine, and a Know/Don't Know
Problem",
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A proof was claimed in 2017 by Agama and Gensel, but this was later found to be flawed.
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177:. Lemoine's conjecture is that this sequence contains no zeros after the first three.
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130:> 2. The Lemoine conjecture is similar to but stronger than
154:
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Sun, Zhi-Wei. "On sums of primes and triangular numbers."
155:
sequence A046927 (Number of ways to express 2
51:
greater than 5 can be represented as the sum of an odd
333:L. Hodges, "A lesser-known Goldbach conjecture",
150:The number of ways this can be done is given by
146:47 = 13 + 2Ă—17 = 37 + 2Ă—5 = 41 + 2Ă—3 = 43 + 2Ă—2.
428:
8:
219:
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71:in 1895, but was erroneously attributed by
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421:
413:
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263:"Lemoine's Conjecture Verified to 10^10"
213:
323:H. Levy, "On Goldbach's Conjecture",
7:
202:Lemoine's conjecture and extensions
630:Unsolved problems in number theory
392:New York: Springer-Verlag 2004: C1
390:Unsolved Problems in Number Theory
25:
310:L'intermédiare des mathématiciens
118:always has a solution in primes
625:Conjectures about prime numbers
367:(4) (Sep., 1985), pp. 195–203.
126:(not necessarily distinct) for
407:Wolfram Demonstrations Project
250:arXiv preprint arXiv:0803.3737
79:who pondered it in the 1960s.
1:
67:The conjecture was posed by
646:
132:Goldbach's weak conjecture
106:To put it algebraically, 2
448:
443:Prime number conjectures
82:A similar conjecture by
594:Schinzel's hypothesis H
620:Additive number theory
18:Levy's conjecture
599:Waring's prime number
405:by Jay Warendorff,
361:Mathematics Magazine
33:Lemoine's conjecture
564:Legendre's constant
229:"Levy's Conjecture"
515:Elliott–Halberstam
500:Chinese hypothesis
316:(1894), 179; ibid
226:Weisstein, Eric W.
47:, states that all
607:
606:
535:Landau's problems
403:Levy's Conjecture
102:Formal definition
41:Levy's conjecture
16:(Redirected from
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453:Hardy–Littlewood
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341:(1993): 45–47.
308:Emile Lemoine,
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397:External links
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386:Richard K. Guy
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265:. 19 June 2019
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35:, named after
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520:Firoozbakht's
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185:According to
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69:Émile Lemoine
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37:Émile Lemoine
34:
30:
29:number theory
19:
568:
485:Bateman–Horn
389:
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320:(1896), 151.
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291:1709.05335v6
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267:. Retrieved
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55:and an even
53:prime number
49:odd integers
40:
32:
26:
579:Oppermann's
525:Gilbreath's
495:Bunyakovsky
330:(1963): 274
175:are primes)
614:Categories
584:Polignac's
557:Twin prime
552:Legendre's
540:Goldbach's
470:Agoh–Giuga
335:Math. Mag.
325:Math. Gaz.
303:References
77:Hyman Levy
45:Hyman Levy
569:Lemoine's
510:Dickson's
490:Brocard's
475:Andrica's
234:MathWorld
187:MathWorld
73:MathWorld
57:semiprime
574:Mersenne
505:Cramér's
196:See also
181:Evidence
43:, after
530:Grimm's
480:Artin's
381:2689513
355:2690477
269:19 June
252:(2008).
138:Example
98:+1) ).
63:History
379:
353:
167:where
159:+1 as
110:+ 1 =
589:PĂłlya
377:JSTOR
351:JSTOR
286:arXiv
208:Notes
545:weak
271:2019
171:and
152:OEIS
122:and
463:2nd
458:1st
369:doi
343:doi
114:+ 2
84:Sun
75:to
59:.
27:In
616::
388:,
375:.
365:58
363:,
349:.
339:66
337:,
328:47
312:,
231:.
216:^
163:+2
134:.
31:,
436:e
429:t
422:v
409:.
371::
345::
318:3
314:1
294:.
288::
273:.
237:.
173:q
169:p
165:q
161:p
157:n
128:n
124:q
120:p
116:q
112:p
108:n
96:x
94:(
92:x
90:+
88:p
20:)
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