منابع مشابه
Small gaps between primes
The twin prime conjecture states that there are infinitely many pairs of distinct primes which differ by 2. Until recently this conjecture had seemed to be out of reach with current techniques. However, in 2013, the author proved that there are infinitely many pairs of distinct primes which differ by no more than B with B = 7 · 107. The value of B has been considerably improved by Polymath8 (a ...
متن کاملGaps between Prime Numbers
Let dn = Pn+i ~Pn denote the nth gap in the sequence of primes. We show that for every fixed integer A; and sufficiently large T the set of limit points of the sequence {(dn/logra, ■ • • ,dn+k-i/logn)} in the cube [0, T]k has Lebesgue measure > c(k)Tk, where c(k) is a positive constant depending only on k. This generalizes a result of Ricci and answers a question of Erdös, who had asked to prov...
متن کاملBounded gaps between primes
It is proved that lim inf n→∞ (pn+1 − pn) < 7× 10, where pn is the n-th prime. Our method is a refinement of the recent work of Goldston, Pintz and Yildirim on the small gaps between consecutive primes. A major ingredient of the proof is a stronger version of the Bombieri-Vinogradov theorem that is applicable when the moduli are free from large prime divisors only (see Theorem 2 below), but it ...
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An excess of events with a rapidity gap between jets, over what would be expected from non-diffractive processes, has been observed at HERA. A process based on a perturbative QCD calculation of colour singlet exchange has been added to HERWIG. With this addition, HERWIG is able to describe the number of events with a gap between jets over the number without a gap. This gap fraction is predicted...
متن کاملLong Gaps between Primes
Let pn denotes the n-th prime. We prove that max p n+16X (pn+1 − pn) ≫ logX log logX log log log logX log log logX for sufficiently large X , improving upon recent bounds of the first three and fifth authors and of the fourth author. Our main new ingredient is a generalization of a hypergraph covering theorem of Pippenger and Spencer, proven using the Rödl nibble method. CONTENTS
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2013
ISSN: 0024-6093
DOI: 10.1112/blms/bdt060