Dario Alpern is collecting factors of googolplex+10 (GP+10 for short). In fact he's collecting factors of 10^10^100+x for x in 0..999. David Broadhurst wrote a pari/gp script to find factors, I've translated it to C and optimised it somewhat. Source is available, as are windows exes and GMP dlls to build from scratch. This page is thrown together in 2 minutes, can you tell?
Programs that are useful:
On 9th August this year, I got this missive from Bertram Felgenhauer via IRC:
19:22 <int-e> Hi, I realize http://fatphil.org/maths/googolplex/ is old enough to vote, but has anybody ever pointed out that you can discard half of the candidates by checking that 10 is a quadratic non-residue modulo q? https://int-e.eu/~bf3/misc/gp+10sq.c implements such a check.I will confess to not having a clue what my old code did, but the logic appears to make immediate sense, and if it didn't, there would be trivially-findable counter-examples by the bucketload in the enormous set of results already found. This I've not done, erm, because <fx sound="flipping excuse calendar" /> I don't even have access to this webserver any more.
20:32 <int-e> Oops, the check should be flipped when k is even (because then q = 1 (mod 4), making -1 a square). I accidentally got this correct in the code, but the reasoning behind it was flawed.
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