Matches in SemOpenAlex for { <https://semopenalex.org/work/W2022773207> ?p ?o ?g. }
Showing items 1 to 63 of
63
with 100 items per page.
- W2022773207 endingPage "873" @default.
- W2022773207 startingPage "863" @default.
- W2022773207 abstract "Define ψ m to be the smallest strong pseudoprime to all the first m prime bases. If we know the exact value of ψ m , we will have, for integers n < ψ m , 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 Pornerance et al. and Jaeschke, ψ m are known for 1 ≤ m ≤ 8. Upper bounds for ψ 9 , ψ 10 and ψ 1 were given by Jaeschke. 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 total 44 such numbers, six of which are also spsp(31), and three numbers are spsp's to both bases 31 and 37. As a result the upper bounds for ψ 10 and ψ 11 are lowered from 28- and 29-decimal-digit numbers to 22-decimal-digit numbers, and a 24-decimal-digit upper bound for ψ 12 is obtained. The 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 pseudoprime to one or to several prime bases. Comparisons of effectiveness with both Jaeschke's and Arnault's methods are given." @default.
- W2022773207 created "2016-06-24" @default.
- W2022773207 creator A5046045131 @default.
- W2022773207 date "2000-02-17" @default.
- W2022773207 modified "2023-10-13" @default.
- W2022773207 title "Finding strong pseudoprimes to several bases" @default.
- W2022773207 cites W1581807437 @default.
- W2022773207 cites W1592261758 @default.
- W2022773207 cites W1970580817 @default.
- W2022773207 cites W1998777945 @default.
- W2022773207 cites W2005989749 @default.
- W2022773207 cites W2008969497 @default.
- W2022773207 cites W2011093758 @default.
- W2022773207 cites W2012857639 @default.
- W2022773207 cites W2030340884 @default.
- W2022773207 cites W2032521550 @default.
- W2022773207 cites W2071593615 @default.
- W2022773207 cites W2077626697 @default.
- W2022773207 cites W2086804846 @default.
- W2022773207 cites W2089613796 @default.
- W2022773207 cites W2329291360 @default.
- W2022773207 cites W2330778380 @default.
- W2022773207 cites W2729188851 @default.
- W2022773207 cites W2791520396 @default.
- W2022773207 cites W3115146178 @default.
- W2022773207 doi "https://doi.org/10.1090/s0025-5718-00-01215-1" @default.
- W2022773207 hasPublicationYear "2000" @default.
- W2022773207 type Work @default.
- W2022773207 sameAs 2022773207 @default.
- W2022773207 citedByCount "20" @default.
- W2022773207 countsByYear W20227732072012 @default.
- W2022773207 countsByYear W20227732072014 @default.
- W2022773207 countsByYear W20227732072020 @default.
- W2022773207 countsByYear W20227732072022 @default.
- W2022773207 crossrefType "journal-article" @default.
- W2022773207 hasAuthorship W2022773207A5046045131 @default.
- W2022773207 hasBestOaLocation W20227732071 @default.
- W2022773207 hasConcept C202444582 @default.
- W2022773207 hasConcept C33923547 @default.
- W2022773207 hasConceptScore W2022773207C202444582 @default.
- W2022773207 hasConceptScore W2022773207C33923547 @default.
- W2022773207 hasIssue "234" @default.
- W2022773207 hasLocation W20227732071 @default.
- W2022773207 hasLocation W20227732072 @default.
- W2022773207 hasOpenAccess W2022773207 @default.
- W2022773207 hasPrimaryLocation W20227732071 @default.
- W2022773207 hasRelatedWork W1557945163 @default.
- W2022773207 hasRelatedWork W1989920940 @default.
- W2022773207 hasRelatedWork W2036077645 @default.
- W2022773207 hasRelatedWork W2096753949 @default.
- W2022773207 hasRelatedWork W2742285599 @default.
- W2022773207 hasRelatedWork W2963103437 @default.
- W2022773207 hasRelatedWork W2963341196 @default.
- W2022773207 hasRelatedWork W2964292522 @default.
- W2022773207 hasRelatedWork W3103780039 @default.
- W2022773207 hasRelatedWork W4249580765 @default.
- W2022773207 hasVolume "70" @default.
- W2022773207 isParatext "false" @default.
- W2022773207 isRetracted "false" @default.
- W2022773207 magId "2022773207" @default.
- W2022773207 workType "article" @default.