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Finding strong pseudoprimes to several bases

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 …

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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 https://bioforcene.com

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

On strong pseudoprimes to several bases (0) - Pennsylvania …

Category:[1509.00864] Strong Pseudoprimes to Twelve Prime Bases - arXiv.org

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Finding strong pseudoprimes to several bases

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WebApr 26, 2024 · The test with a random integer a is called strong pseudoprime test to base a. If the test does not say the number n is composite then n is called a strong pseudoprime … WebFinding strong pseudoprimes to several bases. Mathematics of computing. Discrete mathematics. Mathematical analysis. Numerical analysis. Number-theoretic …

Finding strong pseudoprimes to several bases

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WebSep 16, 2011 · Euler Pseudoprimes for Half of the Bases Authors: Lorenzo Di Biagio Italian National Institute of Statistics Abstract We prove that an odd number is an Euler pseudoprime for exactly one half of... WebApr 26, 2024 · The test with a random integer a is called strong pseudoprime test to base a. If the test does not say the number n is composite then n is called a strong pseudoprime to base a. The set of all strong pseudoprimes to base a is denoted by spsp ( a ).

WebMar 24, 2024 · A composite number passing Miller's test is called a strong pseudoprime to base . If a number does not pass the test, then it is called a witness for the compositeness. If is an odd, positive composite number, then passes Miller's test for at most bases with (Long 1995). There is no analog of Carmichael numbers for strong pseudoprimes . WebFeb 1, 2010 · In this paper we tabulate all strong pseudoprimes (spsp’s) n&lt;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...

WebIf n and 2 n − 1 are primes , where n &gt; 3 , then p = n ⋅ ( 2 n − 1) is a pseudoprime to base 3 . Claim: If p is an odd prime not dividing a 2 − 1, then m := a 2 p − 1 a 2 − 1 is a pseudoprime base a. Proof: We know a p ≡ a mod p, so we also know a 2 p ≡ a 2 mod p. So we know that p ∣ ( a 2 p − a 2). 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 …

WebFeb 17, 2000 · FINDING STRONG PSEUDOPRIMES TO SEVERAL BASES ZHENXIANG ZHANG Dedicated to the memory of P. Erd6's (1913-1996) ABSTRACT. Define Om to …

WebFeb 17, 2000 · FINDING STRONG PSEUDOPRIMES TO SEVERAL BASES ZHENXIANG ZHANG Dedicated to the memory of P. Erd}os (1913{1996) Abstract. De ne mto be the smallest strong pseudoprime to all the rst mprime bases. If we know the exact value of … embroidered holiday giftsWebOct 1, 2003 · Finding C3-strong pseudoprimes. Math. Comput. The main idea of the method is that it loop on candidates of signatures and kernels with heights bounded, … forecast 97WebSep 2, 2015 · We also present an algorithm to find all integers that are strong pseudoprimes to the first prime bases; with a reasonable heuristic assumption we can … forecast 97201