منابع مشابه
The 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 کاملOn 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 کاملComputing the Pseudoprimes up to 10 13
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).
متن کاملThe Distribution of Pseudoprimes
The RSA crypto-system relies on the availability of very large prime numbers. Tests for finding these large primes can be categorized as deterministic and probabilistic. Deterministic tests, such as the Sieve of Erastothenes, offer a 100 percent assurance that the number tested and passed as prime is actually prime. Despite their refusal to err, deterministic tests are generally not used to fin...
متن کاملOn the Distribution of Pseudoprimes
Let 9 (x) denote the pseudoprime counting function. With L(x) = exp{log x log log log x/log log *}> we prove 9(x) < x ■ L(x)~'/2 for large x, an improvement on the 1956 work of Erdös. We conjecture that 9(x) = xL(x)"1+o(1).
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1980
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1980-0572872-7