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[12] Zhang made this claim again in George Csicsery's documentary film "Counting from Infinity: Yitang Zhang and the Twin Prime Conjecture" [13] while discussing his difficulties at Purdue and in the years that followed. [9] Moh claimed that Zhang never came back to him requesting recommendation letters. [11]
A stronger form of the twin prime conjecture, the Hardy–Littlewood conjecture (see below), postulates a distribution law for twin primes akin to the prime number theorem. On 17 April 2013, Yitang Zhang announced a proof that there exists an integer N that is less than 70 million, where there are infinitely many pairs of primes that differ by ...
The main topic of the book is the conjecture that there exist infinitely many twin primes, dating back at least to Alphonse de Polignac (who conjectured more generally in 1849 that every even number appears infinitely often as the difference between two primes), and the significant progress made recently by Yitang Zhang and others on this problem.
In 2013 Yitang Zhang showed [17] that there are infinitely many prime pairs with gap bounded by 70 million, and this result has been improved to gaps of length 246 by a collaborative effort of the Polymath Project. [18]
For the 2013–2014 year, Maynard was a CRM-ISM postdoctoral researcher at the University of Montreal. [7]In November 2013, Maynard gave a different proof of Yitang Zhang's theorem [8] that there are bounded gaps between primes, and resolved a longstanding conjecture by showing that for any there are infinitely many intervals of bounded length containing prime numbers. [9]
As of April 14, 2014, one year after Zhang's announcement, according to the Polymath project wiki, n has been reduced to 246. [6] Further, assuming the Elliott–Halberstam conjecture and its generalized form, the Polymath project wiki states that n has been reduced to 12 and 6, respectively. [7] For n = 2, it is the twin prime conjecture.
Yitang Zhang – mathematician, known for establishing the first finite bound on gaps between prime numbers; Stephen Shing-Toung Yau – Distinguished Professor Emeritus at the University of Illinois at Chicago; Mu-Tao Wang (王慕道) – Professor of Mathematics at Columbia University, received a PhD in Mathematics in 1998 from Harvard University
They used it in 2005 to show that there are infinitely many prime tuples whose distances are arbitrarily smaller than the average distance that follows from the prime number theorem. The sieve was then modified by Yitang Zhang in order to prove a finite bound on the smallest gap between two consecutive primes that is attained infinitely often. [2]