Discover magazine article by steve nadis, prime solver gaps between primes numberphile university of nottingham video shorter version gaps between primes. Zhang, yitang zhang, yi tang 1nhndm bounded gaps between primes. Where can i find the proof of bounded gaps between primes. Unheralded mathematician bridges the prime gap the problem of pairs. A much needed gap is finally found, notices ams, 2015, nr. Yitang zhang proves landmark theorem in distribution of.
In other words, that the gap between one prime and the next is bounded by 70,000,000 infinitely oftenthus, the bounded gaps conjecture. His column at the aperiodical is travels in a mathematical world. 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. The seeds of zhang s result lie in a paper from eight years ago. University of nottingham physicist ed copeland uses a pen and paper to explain yitang zhang s finding on bounded gaps between prime numbers. Bounded gaps between primes yitang zhang abstract it is proved that liminf n. While working for the university of new hampshire as a lecturer, zhang submitted an article to the annals of mathematics in 20 which established the first finite bound on the least gap between consecutive primes that is attained infinitely often. Bounded gaps between primes by yitang zhang, in annals of mathematics. Stony brook mathematics colloquium video bounded gaps between primes yitang zhang university of new hampshireias date. But what yitang zhang just proved is that there are infinitely many pairs of primes that differ by at most 70,000,000. A major ingredient of the proof is a stronger version of the bombierivinogradov theorem that. Alec wilkinson, the pursuit of beauty, yitang zhang solves a puremath mystery, the new yorker, profiles, february 2, 2015 issue.
This can be seen as a massive breakthrough on the subject of twin primes and other. A major ingredient of the proof is a stronger version of the. I want to study the proof, even if i cant fully understand it. Sutherland mit new bounds on gaps between primes october 17, 20 19 28. Gaps between primes extra footage numberphile duration. This gives us an upper bound on hk, hence on the gap. The paper is so beautiful that some mathematicians. Yitang zhang bounded gaps between primes 2014 youtube. Prime numbers those that have no factors other than 1. Where can i find the proof of bounded gaps between primes by yitang zhang. 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. An exciting paper about gaps between prime numbers a step closer to proving the twin prime conjecture. Bounded gaps between primes by yitang zhang abstract it is proved that liminf n. Professor zhang s breakthrough paper, bounded gaps between primes, has solved a pure mathematics problem attempted by mathematicians for more than 150 years, said ucsb chancellor henry t.