Sieve Methods and Gap Between Consecutive Primes

Guria, Rachita (2018) Sieve Methods and Gap Between Consecutive Primes. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Rachita Guria (13MS080)) 13MS080.pdf - Submitted Version Restricted to Repository staff only Download (537kB)

Abstract

I have written an expository article on D. A. Goldston, J. Pintz, and C. Y. Yildirim method for showing that there exist infinitely many prime numbers which are very close to each other. The method depends on the level of distribution of primes in arithmetic progressions and Sieve methods. Assuming the Elliott-Halberstam conjecture, we prove that there are infinitely often primes differing by 16 or less. Unconditionally, we prove that there exist consecutive primes which are closer than any arbitrarily small multiple of the average gap, that is, lim inf (n->∞)pn+1-pn/log pn=0

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