First occurrence prime gaps
نویسندگان
چکیده
منابع مشابه
New maximal prime gaps and first occurrences
The search for first occurrences of prime gaps and maximal prime gaps is extended to 1015. New maximal prime gaps of 806 and 906 are found, and sixty-two previously unpublished first occurrences are found for gaps varying from 676 to 906.
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 کاملLarge Gaps between Consecutive Prime Numbers
Let G(X) denote the size of the largest gap between consecutive primes below X . Answering a question of Erdős, we show that G(X) > f(X) logX log logX log log log logX (log log logX) , where f(X) is a function tending to infinity with X . Our proof combines existing arguments with a random construction covering a set of primes by arithmetic progressions. As such, we rely on recent work on the e...
متن کاملFinding prime pairs with particular gaps
By a prime gap of size g, we mean that there are primes p and p + g such that the g − 1 numbers between p and p + g are all composite. It is widely believed that infinitely many prime gaps of size g exist for all even integers g. However, it had not previously been known whether a prime gap of size 1000 existed. The objective of this article was to be the first to find a prime gap of size 1000,...
متن کاملNotes on Zhang’s Prime Gaps Paper
This result is deduced from the following result. Call an admissible set to be a finite set of integers H which avoids at least one residue class modulo p for each prime p. For any natural number k0, let Q(k0) denote the assertion that for any admissible set H of integers of cardinality k0, there are infinitely many translates n +H of H that contain at least two primes. Note that if H is an adm...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1989
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1989-0947470-1