Finding strong pseudoprimes to several bases
WebJun 1, 2024 · The ability of the test to determine prime integers is based on the difference of the number of primality witnesses for composite and prime integers. Let W ( n ) denote the set of all primality... WebAt last we speed our algorithm for finding larger $C_3$-spsp’s, say up to $10^ {50}$, with a given signature to more prime bases. Comparisons of effectiveness with Arnault’s and our previous methods for finding $C_3$-strong pseudoprimes to the first several prime bases are given. References Similar Articles Additional Information
Finding strong pseudoprimes to several bases
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WebApr 1, 2005 · We conjecture that there exist no C3-spsp's < 1024 to the first 12 prime bases with heights ≥ 10 9 and so that ψ12 = 3186 65857 83403 11511 67461 (24 digits) = 399165290221 ·798330580441, which... WebFinding strong pseudoprimes to several bases. Mathematics of computing. Discrete mathematics. Mathematical analysis. Numerical analysis. Number-theoretic computations. Comments. Login options. Check if you have access through your login credentials or your institution to get full access on this article. ...
WebMar 24, 2024 · A primality test that provides an efficient probabilistic algorithm for determining if a given number is prime. It is based on the properties of strong pseudoprimes. The algorithm proceeds as follows. Given an odd integer n, let n=2^rs+1 with s odd. Then choose a random integer a with 1<=a<=n-1. If a^s=1 (mod n) or … WebJan 1, 2002 · Finding strong pseudoprimes to several bases. II October 2003 · Mathematics of Computation Zhenxiang Zhang Min Tang ... [Show full abstract] October 1975 Nigel J. Keen The aperture efficiency of...
WebA strong pseudoprime to base a is always an Euler–Jacobi pseudoprime, an Euler pseudoprime and a Fermat pseudoprime to that base, but not all Euler and Fermat … WebFinding strong pseudoprimes to several bases (0) by Zhenxiang Zhang, Min Tang Venue: II. Math. Comp: Add To MetaCart. Tools. Sorted by: Results 1 - 9 of 9. Prime numbers: a computational perspective. Second Edition by Richard Crandall, Carl Pomerance, Richard ...
WebZhang’s paper shows how to find a much smaller number of composite numbers that might be strong pseudoprimes. He picks numbers k > 1, then picks primes q such that q is larger than the largest prime factor of k, and kq < 10^9. He also cites other papers that show the first strong pseudo prime that isn’t square free must be very large.
WebThe Baillie–PSW test is a combination of a strong Fermat probable prime test (that means Miller-Rabin) to base 2 and a strong Lucas probable prime test. The Fermat and Lucas test each have their own list of pseudoprimes, that is, composite numbers that pass the test. For example, the first ten strong pseudoprimes to base 2 are temperatura em taubatéWebSep 2, 2015 · Strong Pseudoprimes to Twelve Prime Bases. Jonathan P. Sorenson, Jonathan Webster. Let be the smallest strong pseudoprime to the first prime bases. This value is known for . We extend this by finding and . We also present an algorithm to find all integers that are strong pseudoprimes to the first prime bases; with a reasonable … temperatura em turku finlandia hojeWebOct 1, 2003 · We conjecture that ψ9 = ψ10 = ψ11 = 3825 12305 65464 13051, and give reasons to support this conjecture. The main idea for finding these Carmichael numbers … temperatura em ubatuba spWebIf you want a bit better results, you could create a sieve of pseudo-primes for the first 20 primes, then you can quickly check which set of 10 gets you furthest, and then you can check larger bases to see which ones will catch the few counterexamples that you have. temperatura em ubatuba hojeWebApr 1, 2001 · Finding strong pseudoprimes to several bases. Author: Zhenxiang Zhang ... temperatura em uberaba minas geraisWebFinding strong pseudoprimes to several bases; article . Free Access. Finding strong pseudoprimes to several bases. Author: Zhenxiang Zhang. View Profile. Authors Info & … temperatura em uberabaWebApr 1, 2001 · In this paper we tabulate all strong pseudoprimes (spsp’s) n<10 24 to the first ten prime bases 2,3,⋯,29, which have the form n=pq with p,q odd primes and q-1=k (p-1), k=2,3,4· There are in... temperatura em uberaba agora