منابع مشابه
The Pseudosquares Prime Sieve
We present the pseudosquares prime sieve, which finds all primes up to n. Define p to be the smallest prime such that the pseudosquare Lp > n/(π(p)(logn)); here π(x) is the prime counting function. Our algorithm requires only O(π(p)n) arithmetic operations and O(π(p) log n) space. It uses the pseudosquares primality test of Lukes, Patterson, and Williams. Under the assumption of the Extended Ri...
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Let $R$ be a commutative ring with identity. A proper ideal $P$ of $R$ is a $(n-1,n)$-$Phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin R$, $a_1cdots a_nin Pbackslash P^m$ ($a_1cdots a_nin Pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin P$, for some $iin{1,ldots,n}$; ($m,ngeq 2$). In this paper several results concerning $(n-1,n)$-$Phi_m$-prime and $(n-1,n)$-...
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We present a new algorithm that nds all primes up to n using at most O(n= log log n) arithmetic operations and O(n=(log n log log n)) space. This algorithm is an improvement of a linear prime number sieve due to Pritchard. Our new algorithm matches the running time of the best previous prime number sieve, but uses less space by a factor of (log n). In addition, we present the results of our imp...
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متن کاملon generalisations of almost prime and weakly prime ideals
let $r$ be a commutative ring with identity. a proper ideal $p$ of $r$ is a $(n-1,n)$-$phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin r$, $a_1cdots a_nin pbackslash p^m$ ($a_1cdots a_nin pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin p$, for some $iin{1,ldots,n}$; ($m,ngeq 2$). in this paper several results concerning $(n-1,n)$-$phi_m$-prime and $(n-1,n)$-...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1978
ISSN: 0022-314X
DOI: 10.1016/0022-314x(78)90038-0