Correction to “large prime factors of binary forms”
نویسندگان
چکیده
منابع مشابه
Prime sieves using binary quadratic forms
We introduce an algorithm that computes the prime numbers up to N using O(N/log logN) additions and N1/2+o(1) bits of memory. The algorithm enumerates representations of integers by certain binary quadratic forms. We present implementation results for this algorithm and one of the best previous algorithms.
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For F ∈ Z[X], let ΨF (x, y) denote the number of positive integers n not exceeding x such that F (n) is free of prime factors > y. Our main purpose is to obtain lower bounds of the form ΨF (x, y) x for arbitrary F and for y equal to a suitable power of x. Our proofs rest on some results and methods of two articles by the third author concerning localization of divisors of polynomial values. Ana...
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Deene (x;y) to be the number of positive integers n x such that n has no prime divisor larger than y. We present a simple algorithm that approximates (x; y) in O(yf log log x log y + 1 log log y g) oating point operations. This algorithm is based directly on a theorem of Hildebrand and Tenenbaum. We also present data which indicate that this algorithm is more accurate in practice than other kno...
متن کاملBinary Prime Tableau Sequences
This paper proposes a new class of random sequences called binary primes tableau (PT) sequences that have potential applications in cryptography and communications. The PT sequence of rank p is obtained from numbers arranged in a tableau with p columns where primes are marked off until each column has at least one prime and where the column entries are added modulo 2. We also examine the dual t...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1977
ISSN: 0022-314X
DOI: 10.1016/0022-314x(77)90015-4