SYLOW p-PSEUDOPRIMES TO SEVERAL BASES FOR SEVERAL PRIMES p
نویسندگان
چکیده
منابع مشابه
Finding strong pseudoprimes to several bases II
Define ψm to be the smallest strong pseudoprime to all the first m prime bases. If we know the exact value of ψm, we will have, for integers n < ψm, a deterministic efficient primality testing algorithm which is easy to implement. Thanks to Pomerance et al. and Jaeschke, the ψm are known for 1 ≤ m ≤ 8. Upper bounds for ψ9, ψ10 and ψ11 were first given by Jaeschke, and those for ψ10 and ψ11 were...
متن کاملFinding strong pseudoprimes to several bases
Define ψm to be the smallest strong pseudoprime to all the first m prime bases. If we know the exact value of ψm, we will have, for integers n < ψm, a deterministic primality testing algorithm which is not only easier to implement but also faster than either the Jacobi sum test or the elliptic curve test. Thanks to Pomerance et al. and Jaeschke, ψm are known for 1 ≤ m ≤ 8. Upper bounds for ψ9, ...
متن کاملARE PSEUDOPRIMES FOR ALMOST ALL PRIMES p
It was proven by Emma Lehmer that for almost all odd primes p, F2p is a Fibonacci pseudoprime. In this paper, we generalize this result to Lucas sequences {Uk}. In particular, we find Lucas sequences {Uk} for which either U2p is a Lucas pseudoprime for almost all odd primes p or Up is a Lucas pseudoprime for almost all odd primes p.
متن کاملNotes on some new kinds of pseudoprimes
J. Browkin defined in his recent paper (Math. Comp. 73 (2004), pp. 1031–1037) some new kinds of pseudoprimes, called Sylow p-pseudoprimes and elementary Abelian p-pseudoprimes. He gave examples of strong pseudoprimes to many bases which are not Sylow p-pseudoprime to two bases only, where p = 2 or 3. In this paper, in contrast to Browkin’s examples, we give facts and examples which are unfavora...
متن کاملSome new kinds of pseudoprimes
We define some new kinds of pseudoprimes to several bases, which generalize strong pseudoprimes. We call them Sylow p-pseudoprimes and elementary Abelian p-pseudoprimes. It turns out that every n < 1012, which is a strong pseudoprime to bases 2, 3 and 5, is not a Sylow p-pseudoprime to two of these bases for an appropriate prime p|n− 1. We also give examples of strong pseudoprimes to many bases...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2009
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972709000744