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Goldston, S. W. Graham, Pintz, and Yıldırım proved that the difference between numbers which are products of exactly 2 primes is infinitely often at most 6.
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that are closer to each other than the average distance between consecutive primes by a factor of ε, i.e.,
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but was later retracted. Pintz joined the team and completed the proof in 2005 and developed the so called
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325:, then one can also show that primes within 16 of each other occur infinitely often, which is nearly the
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by showing that every sufficiently large even number is the sum of two primes and at most 8 powers of 2.
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D. Goldston, S. W. Graham, J. Pintz, C. Yıldırım: Small gaps between products of two primes,
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Komlós, J.; Pintz, J.; Szemerédi, E. (1982), "A lower bound for
Heilbronn's problem",
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183:{\displaystyle \liminf _{n\to \infty }{\frac {p_{n+1}-p_{n}}{\log p_{n}}}=0}
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Pintz, János (1987). "An effective disproof of the
Mertens conjecture".
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Pintz gave an effective upper bound for the first number for which the
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Iwaniec, Henryk; Pintz, János (1984). "Primes in short intervals".
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Goldston, Daniel; Pintz, János; Yıldırım, Cem (1 September 2009).
385:) upper bound for the number of those numbers that are less than
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321:) occurs infinitely often. Further, if one assumes the
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276:. This result was originally reported in 2003 by
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719:Institute for Advanced Study visiting scholars
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690:Alfréd Rényi Institute of Mathematics
41:
7:
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267: < ε log
729:Eötvös Loránd University alumni
449:Magyar és nemzetközi ki kicsoda
447:Peter Hermann, Antal Pasztor:
389:and not the sum of two primes.
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1:
699:Mathematics Genealogy Project
512:"Bounded gaps between primes"
323:Elliott–Halberstam conjecture
75:American Mathematical Society
67:Hungarian Academy of Sciences
734:Mathematicians from Budapest
510:Zhang, Yitang (1 May 2014).
65:and is also a member of the
63:Rényi Mathematical Institute
31:when mentioning individuals.
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480:10.4007/annals.2009.170.819
69:. In 2014, he received the
46:; born 20 December 1950 in
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617:Monatshefte für Mathematik
396:, he improved a result of
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359:there is a prime between
424:Fazekas Mihály Gimnázium
61:. He is a fellow of the
39:Hungarian pronunciation:
27:. This article uses
19:The native form of this
602:10.1112/jlms/s2-25.1.13
43:[ˈjaːnoʃˈpints]
16:Hungarian mathematician
666:Proc. Lond. Math. Soc.
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59:analytic number theory
516:Annals of Mathematics
467:Annals of Mathematics
327:twin prime conjecture
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215:{\displaystyle p_{n}}
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463:"Primes in tuples I"
346:Heilbronn conjecture
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81:Mathematical results
654:. 147–148: 325–333.
344:, he disproved the
317:(log log
686:János Pintz's page
629:10.1007/BF01637280
376:Mertens conjecture
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29:Western name order
419:Landau's problems
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558:on 2009-02-20
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586:(1): 13–24,
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91:Cem Yıldırım
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754:1950 births
695:János Pintz
57:working in
35:János Pintz
25:Pintz János
708:Categories
652:Astérisque
562:2009-03-31
435:References
71:Cole Prize
637:0026-9255
588:CiteSeerX
538:0003-486X
489:0003-486X
414:Prime gap
311:log
286:GPY sieve
159:
141:−
117:∞
114:→
52:Hungarian
408:See also
48:Budapest
697:at the
688:at the
497:1994756
353:Iwaniec
309:√
93:) that
73:of the
50:) is a
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451:, 1994
398:Linnik
378:fails.
195:where
493:S2CID
392:With
351:With
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633:ISSN
534:ISSN
485:ISSN
363:and
340:and
280:and
238:and
89:and
625:doi
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520:179
475:doi
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23:is
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