Computing the Pseudoprimes up to 10 13
نویسنده
چکیده
The paper extends the current known tables of Fermat’s pseudoprimes to base 3 with the bound of 10. The paper is motivated by works of C. Pomerance (1980), G. E. Pinch (2000), William Galway (2002) and Jan Feitsma (2009) who provided tables of pseudoprimes with base 2 up to 10 (Pinch), 10 (Galway) and 10 (Feitsma).
منابع مشابه
On the Distributions of Pseudoprimes, Carmichael Numbers, and Strong Pseudoprimes
Building upon the work of Carl Pomerance and others, the central purpose of this discourse is to discuss the distribution of base-2 pseudoprimes, as well as improve upon Pomerance's conjecture regarding the Carmichael number counting function [8]. All conjectured formulas apply to any base b ≥ 2 for x ≥ x0(b). A table of base-2 pseudoprime, 2-strong pseudoprime, and Carmichael number counts up ...
متن کاملPseudoprimes for Higher-order Linear Recurrence Sequences
With the advent of high-speed computing, there is a rekindled interest in the problem of determining when a given whole number N > 1 is prime or composite. While complex algorithms have been developed to settle this for 200-digit numbers in a matter of minutes with a supercomputer, there is a need for simpler, more practical algorithms for dealing with numbers of a more modest size. Such practi...
متن کاملNotes on some new kinds of pseudoprimes
J. Browkin defined in his recent paper (Math. Comp. 73 (2004), pp. 1031–1037) some new kinds of pseudoprimes, called Sylow p-pseudoprimes and elementary Abelian p-pseudoprimes. He gave examples of strong pseudoprimes to many bases which are not Sylow p-pseudoprime to two bases only, where p = 2 or 3. In this paper, in contrast to Browkin’s examples, we give facts and examples which are unfavora...
متن کاملCipolla Pseudoprimes
We consider the pseudoprimes that M. Cipolla constructed. We call such pseudoprimes Cipolla pseudoprimes. In this paper we find infinitely many Lucas and Lehmer pseudoprimes that are analogous to Cipolla pseudoprimes.
متن کاملThe Pseudoprimes to 25 • 109
The odd composite n < 25 • 10 such that 2n_1 = 1 (mod n) have been determined and their distribution tabulated. We investigate the properties of three special types of pseudoprimes: Euler pseudoprimes, strong pseudoprimes, and Carmichael numbers. The theoretical upper bound and the heuristic lower bound due to Erdös for the counting function of the Carmichael numbers are both sharpened. Several...
متن کامل