Phil Karn [density of Carmichael numbers?] I have a vague recollection of the number of Carmichael numbers less than N being N^(2/7). Thus, the number of 1000-bit Carmichael numbers is (2^1001)^(2/7) - (2^1000)^(2/7) = 2^286 - 2^(2000/7) = 2^285*(2-2^(5/7)) =~ 2.2 x 10^86 I make no claims that this information is correct. -Ray -- Ray Cromwell | Engineering is the implementation of science; -- -- rjc@gnu.ai.mit.edu | politics is the implementation of faith. --