Constructing Carmichael numbers through improved subset-product algorithms

Autor:	Alford, W. R., Grantham, Jon, Hayman, Steven, Shallue, Andrew
Rok vydání:	2012
Předmět:	Mathematics - Number Theory 11Y16
Zdroj:	Math. Comp. 83 (2014), no. 286, 899-915
Druh dokumentu:	Working Paper
Popis:	We have constructed a Carmichael number with 10,333,229,505 prime factors, and have also constructed Carmichael numbers with k prime factors for every k between 3 and 19,565,220. These computations are the product of implementations of two new algorithms for the subset product problem that exploit the non-uniform distribution of primes p with the property that p-1 divides a highly composite \Lambda. Comment: Table 1 fixed; previously the last 30 digits and number of digits were calculated incorrectly
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1203.6664 Zobrazit plný text záznamu View this record from Arxiv