On 4/30/2013 8:06 PM, Bill Gosper wrote:
Wow. Nice. It appears that the base 2 6.7x10^15 search https://cs.uwaterloo.ca/journals/JIS/VOL14/Klyve/klyve3.html omitted pseudoprimes. A moronic Mma search thru 5.7G is so far fruitless. Has no one tried this before? --rwg
Any prime divisor of a "Wieferich pseudoprime" (i.e., a composite n such that 2^n == 2 (mod n^2)) must itself be a Wieferich prime. A proof can be found here (of all places): http://forums.xkcd.com/viewtopic.php?t=23397&p=699486
Is it obvious that if n∈N and 2==Mod[2^n,n^2] then n is (a Wieferich) prime? Why don't we just call A001220 Wieferich numbers? --rwg
The term "Wieferich number" has been used for n such that 2^phi(n) == 1 (mod n^2); see A077816. -- Fred W. Helenius fredh@ix.netcom.com