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. ...
متن کاملThe Large Sieve for 2 modulo Primes
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.
متن کاملOn Bombieri’s Asymptotic Sieve
If a sequence (an) of non-negative real numbers has “best possible” distribution in arithmetic progressions, Bombieri showed that one can deduce an asymptotic formula for the sum ∑ n≤x anΛk(n) for k ≥ 2. By constructing appropriate sequences, we show that any weakening of the welldistribution property is not sufficient to deduce the same conclusion.
متن کاملImplementing the Hypercube Quadriatic Sieve with Two Large Primes
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...
متن کاملOn the Small Sieve . I . Sifting by Primes
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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ژورنال
عنوان ژورنال: The Annals of Mathematics
سال: 1998
ISSN: 0003-486X
DOI: 10.2307/121035