منابع مشابه
Asymptotic sieve for primes
For a long time it was believed that sieve methods might be incapable of achieving the goal for which they had been created, the detection of prime numbers. Indeed, it was shown [S], [B] to be inevitable that, in the sieve’s original framework, no such result was possible although one could come tantalizingly close. This general limitation is recognized as the “parity problem” of sieve theory. ...
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Let λ be a fixed integer, λ ≥ 2. Let s n be any strictly increasing sequence of positive integers satisfying s n ≤ n 15/14+o(1). In this paper we give a version of the large sieve inequality for the sequence λ sn. In particular, we prove that for π(X)(1 + o(1)) primes p, p ≤ X, the numbers λ sn , n ≤ X(log X) 2+ε are uniformly distributed modulo p.
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This paper deals with variations of the Quadratic Sieve integer factoring algorithm. We describe what we believe is the rst implementation of the Hypercube Multiple Polynomial Quadratic Sieve with two large primes, We have used this program to factor many integers with up to 116 digits. Our program appears to be many times faster than the (non-hypercube) Multiple Polynomial Quadratic Sieve with...
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The main object of the paper is to prove that if P is a set of primes with sum of reciprocals _cx, where c is a positive constant depending only on K. A lower estimate is given for c and a similar result is achieved in the case when the condition of primality is substituted by the weaker condition that any m elem...
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denote the the maximum gap between consecutive primes less than X . It is clear from the prime number theorem that G(X) > (1 + o(1)) logX, as the average gap between the prime numbers which are 6 X is ∼ logX . Explicit gaps of (at least) this size may be constructed by observing that P (n)+2, P (n)+3, . . . , P (n)+n is a sequence of n−1 composite numbers, where P (n) is the product of the prim...
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ژورنال
عنوان ژورنال: Nature
سال: 1897
ISSN: 0028-0836,1476-4687
DOI: 10.1038/056010b0