Finding strong pseudoprimes to several bases
WebApr 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... WebStrong pseudoprimes to twelve prime bases HTML articles powered by AMS MathViewer by Jonathan Sorenson and Jonathan Webster PDF Math. Comp. 86 (2024), 985-1003 Request permission Abstract: Let ψ m be the smallest strong pseudoprime to the first m prime bases. This value is known for 1 ≤ m ≤ 11. We extend this by finding ψ 12 and ψ 13.
Finding strong pseudoprimes to several bases
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WebIn particular, Zhang gave a Sylowp-pseudoprime (with 27 decimal digits) to the first 6 prime bases for all the first 6 primes p, and conjectured that for any k≥1, there would exist Sylow p-pseudoprimes to the first kprime bases for all the first kprimes p. WebFinding strong pseudoprimes to several bases. Mathematics of computing. Discrete mathematics. Mathematical analysis. Numerical analysis. Number-theoretic …
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 … 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
WebMay 26, 1999 · that there are only 101 strong pseudoprimes for the bases 2, 3, and 5 less than , nine if 7 is added, and none if 11 Also, the bases 2, 13, 23, and 1662803 have no exceptions up to . If is Composite, then there is a base for … 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. ...
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 ...
WebMar 24, 2024 · A strong pseudoprime to the base is also an Euler pseudoprime to the base (Pomerance et al. 1980). The strong pseudoprimes include some Euler … reading salvation armyWebSep 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 … how to survive in dubaiWebThe 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 reading safety glasses 2.0reading sale houseWebIn this paper, we first follow the first author’s previous work to use biquadratic residue characters and cubic residue characters as main tools to tabulate all strong … reading sample test for ielts academicWebIn this paper we tabulate all strong pseudoprimes (spsp’s) n<1024 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 total 44 such numbers, six of which are also spsp(31), and three numbers are spsp’s to both bases 31 and 37. reading sats 2019WebShow 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 ... reading salon at university