# 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 | Kmax | Searcher | Status |

0 | 101 | David Broadhurst | Done |

11 | 5167 | Phil Carmody | Done |

5168 | 10000 | Patrick Demichel | Done |

10000 | 14000 | Norm Dresner |
1135 |

14000 | 18000 | John Gamble |
852 |

18000 | 20000 | Phil Carmody |
376 |

20000 | 30000 | Patrick Demichel |
1365 |

30000 | 40000 | Paul Leyland |
957 |

40000 | 100000 | Patrick Demichel |
3051 |

100000 | 200000 | Patrick Demichel |
2331 |

200000 | 300000 | Patrick Demichel |
1421 |

300000 | 400000 | Patrick Demichel |
954 |

400000 | 500000 | Patrick Demichel |
755 |

500000 | 600000 | Patrick Demichel |
611 |

600000 | 1300000 | Patrick Demichel |
3121 |

1300000 | 2000000 | Patrick Demichel |
1422 |

2000000 | 3100000 | Patrick 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

Another hastily constructed page by Phil Carmody

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