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 29, 2016 · In special cases, the number of bases can easily be calculated, for example the case n = ( 4 k + 3) ( 8 k + 5) , where 4 k + 3 and 8 k + 5 are primes, we have ϕ ( n) 4 …
(PDF) Finding strong pseudoprimes to several bases
WebShow that the composite number 1281 is a strong pseudoprime base 41. "$n-1=2^rm$, then n is a strong pseudoprime base b if either $b^m=1modn$ or $b^{2^sm}=-1modn$" Ok ... 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. embroidered holiday dress
Baillie–PSW primality test - Wikipedia
WebThe main tools used in our methods are the biquadratic residue characters and cubic residue characters. We propose necessary conditions for n to be a strong … WebMar 24, 2024 · Carmichael numbers are odd composite numbers that are Fermat pseudoprimes to every base; they are sometimes called absolute pseudoprimes. The following table gives the number of Poulet numbers psp(2), Euler-Jacobi pseudoprimes ejpsp(2), and strong pseudoprimes spsp(2) to the base 2, and Carmichael numbers … WebApr 1, 2001 · Finding strong pseudoprimes to several bases. Author: Zhenxiang Zhang ... embroidered holiday cards