Factoring GP+10

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?

Table of ranges that have been speculatively reserved

Kmin KmaxSearcher Status
0 101David BroadhurstDone
11 5167Phil Carmody Done
516810000Patrick DemichelDone
1000014000Norm Dresner 1135
1400018000John Gamble 852
1800020000Phil Carmody 376
2000030000Patrick Demichel 1365
3000040000Paul Leyland 957
40000100000Patrick Demichel 3051
100000200000Patrick Demichel 2331
200000300000Patrick Demichel 1421
300000400000Patrick Demichel 954
400000500000Patrick Demichel 755
500000600000Patrick Demichel 611
6000001300000Patrick Demichel 3121
13000002000000Patrick Demichel 1422
20000003100000Patrick Demichel 1414

Resources

Programs that are useful:

Note - the windows executable is unable to go beyond k=48000, as it will overflow. The source is fixed though.

Update: 2020-08-27

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.
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.
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.

Page last knowingly updated: 2020-08-27

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