On the Counting Function of Elliptic Carmichael Numbers
نویسندگان
چکیده
منابع مشابه
Infinitude of Elliptic Carmichael Numbers
In 1987, Gordon gave an integer primality condition similar to the familiar test based on Fermat’s little theorem, but based instead on the arithmetic of elliptic curves with complex multiplication. We prove the existence of infinitely many composite numbers simultaneously passing all elliptic curve primality tests assuming a weak form of a standard conjecture on the bound on the least prime in...
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Let As be the product of the first s primes, let Ps be the set of primes p for which p−1 divides As but p does not divide As, and let Cs be the set of Carmichael numbers n such that n is composed entirely of the primes in Ps and such that As divides n − 1. Erdős argued that, for any ε > 0 and all sufficiently large x (depending on the choice of ε), the set Cs contains more than x1−ε Carmichael ...
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Pomerance conjectured that there are x 1− {1+o(1)} log log log x log log x Carmichael numbers up to x. At the time, his data tables up to 25 · 109 appeared to support his conjecture. However, Pinch extended this data and showed that up to 1021, Pomerance's conjecture did not appear well-supported. Thus, we build upon the work of Carl Pomerance and others to formulate an alternative conjecture r...
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ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 2014
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-2012-037-4