Yitang zhang proves weak version of twin prime conjecture. Zhangs work also set off a flurry of followup activity in the mathematics community, including a collaboration of a dozen or so mathematicians called the polymath8 project, which is attempting to reduce the maximum separation between primes in zhangs proof to something less than 70 million. We give a short introduction to the recent breakthrough theorem of yitang zhang that there are infinitely many pairs of distinct primes p, q with p. Lo yang for information about chengbiao pan quoted below, prof. Bounded gaps between primes by yitang zhang now available.
We have completed our study of the paper bounded gaps between primes by yitang zhang. Because zhang was a nobody at a relatively unknown researchwise us university. Last year, in a breakthrough work of yitang zhang, it was shown that there were infinitely many gaps between primes of bounded size. Recently, yitang zhang proved the existence of a nite bound bsuch that there are in nitely many pairs p n. Pdf new developments on the twin prime problem and. Bounded gaps between primes by yitang zhang abstract it is proved that liminf n. A major ingredient of the proof is a stronger version of the bombierivinogradov theorem that is applicable when the moduli are free from large prime divisors only, but it is adequate for our purpose. He was a math instructor, not a tenuretrack professor, at the university of new hampshire from 1999 to 20, teaching prealgebra and calculus yitang zhang on rat. It began in april 20 when yitang tom zhang, a virtually unknown mathematician working as an adjunct professor at the university of new hampshire, submitted a paper to the annals of mathematics. How yitang tom zhang proved a theorem that had stumped. Conjecture of twin primes still unsolved problem in number theory. So, if the twin prime conjecture is true, it means the gap doesnt get larger, because theres always neighbor primes with gap of just 2.
On the same day, in a lecture at harvard university, yitang tom zhang of the university of new hampshire in durham sketched a proof that there are infinitely many prime numbers separated by less than 70 million. Yitang zhang in celebration of yitang zhang s recent result, consider the gaps between one prime and the next. The big experts in the field had already tried to make this approach work, granville said. Our method is a re nement of the recent work of goldston, pintz and y ld r m on the small gaps between consecutive primes. All large primes have a last digit of 1, 3, 7, or 9, with a 25% proportion of primes having each of these digits. Bounded gaps between primes andrew granville abstract. In his paper, titled bounded gaps between primes and bearing his name alone, zhang attacked the problem by proving that the number of primes that are less than 70 million units apart is. A major ingredient of the proof is a stronger version of the bombierivinogradov theorem that.
Pdf conjecture of twin primes still unsolved problem in. Counting from infinity yitang zhang and the twin prime conjecture a film by george csicsery in april 20, a lecturer at the university of new hampshire submi ed a paper to the annals of mathema cs within weeks word spread. Zhang had made an important breakthrough in number theory by solving. All large odd numbers can be expressed as the sum of three primes. On april 17, a paper arrived in the inbox of annals of mathematics, one of the disciplines preeminent journals. Zhangs original bound here was 70 million, but it has since been cut down to 246 thanks to the efforts of james maynard and an online collaborative polymath project. Zhang, yitang zhang, yi tang 1nhndm bounded gaps between primes. Mathematician yitang zhang, 2014 macarthur fellow youtube. Yitang zhangs techniques for bounding the gaps between primes soon led to rapid progress by the polymath group, and a further innovation by james maynard. Philosophy behind yitang zhangs work on the twin primes. This can be seen as a massive breakthrough on the subject of twin primes and other.
A year ago april, the editors of the annals of mathematics, a journal published by the institute and princeton university, received an email with a submission by an unknown mathematician. Hes not a known expert, but he succeeded where all the experts had failed. This better approximation gives a prediction that the number of twin primes less than a quadrillion should be about 1. Are there any experts here who can explain the proof. Yitang zhang and the twin prime conjecture centers on an exciting string of mathematical discoveries. Yitang zhang bounded gaps between primes 2014 youtube. In a recent paper zha in the annals of mathematics, yitang zhang. An unknown mathematician, yitang zhang, has revolutionized his field and helped move forward a 2,000yearold conjecture about prime numbers. His counterintuitive findings show that special pairs. Why did seemingly nobody notice yitang zhang before the. Within weeks word spread a littleknown mathematician, with. I started a careful study of the paper but stopped after already stumbling over lemma 2. Yitang zhang is a mathematician tackling truly hard questions in number theory leading to the first finite bound on a gap between prime numbers and the best possible qualitative approximation of.
Within weeks word spreada littleknown mathematician, with no permanent job, working in complete isolation had made an important breakthrough towards solving the twin prime conjecture. Aperiodic to complete the story started as a rumour report in primes gotta stick together and confirmed in primes really do stick together, here we report that annals of mathematics has posted the pdf of. The twin prime conjecture states that there are an infinite number of twin primes prime numbers where one prime is two greater than the other. Is the outline in the annals the preprint or the full accepted paper. Bounded gaps between primes yitang zhang abstract it is proved that liminf n. Two proofs spark a prime week for number theory science. Stony brook mathematics colloquium video bounded gaps between primes yitang zhang university of new hampshireias date. Has anybody read yitang zhangs paper on prime gaps.
Yuan wang for detailed information on results related to the twin prime conjecture, and prof. Bounded gaps between primes yitang zhang it is proved that liminf n. Editors of prominent mathematics journals are used to fielding grandiose claims from obscure authors, but this paper was different. An expository essay article pdf available in surveys in mathematics and its applications 122017. Yitang zhang recently published a new attack on the twin primes conjecture. Shiuyuen cheng for pointing out the paper of soundararajan cited in this article, prof. Premiering saturday, may 6 at 1pm on thirteen, counting from infinity. Our method is a refinement of the recent work of goldston, pintz and y. Yitang zhangs pursuit of beauty in math the new yorker. They may not be twin primes, but at least they are 70millionth cousins.
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