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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.

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    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

    Item Type: Thesis (Masters)
    Additional Information: Supervisors: Dr. Subrata Shyam Roy and Dr. Satadal Ganguly
    Uncontrolled Keywords: Consecutive Primes; Elliott-Halberstam Conjecture; Prime Numbers; Sieve Method
    Subjects: Q Science > QA Mathematics
    Divisions: Department of Mathematics and Statistics
    Depositing User: IISER Kolkata Librarian
    Date Deposited: 01 Jan 2019 11:55
    Last Modified: 01 Jan 2019 11:55
    URI: http://eprints.iiserkol.ac.in/id/eprint/804

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