Picture Prime

Description of a 100000-digit prime with text pictured in the digits.

Decimal expansion of the prime N with 50 digits per line.
First 70000 digits of N with every "1" replaced by ".". The last 30000 digits could not be chosen freely. They were determined by the need for N+1 factors.
Prime factors of N+1 with 50 digits per line.
"1" replaced by "." in 30 titanic factors. Proved by Marcel Martin's Primo.
The factors give 30.00% factorization of N+1, exactly what is needed for a Konyagin-Pomerance primality proof (PrimeForm/GW would need 33.33% for a BLS proof).

The prime was found in July 2005 in a distributed project by PrimeForm e-group.
Picture design by Paul Underwood.
Primo primality proofs of N+1 factors and sieving to 10^12 by Jens Kruse Andersen.
PrimeForm/GW prp tests by Jens Kruse Andersen, James Chislett, Jason Earls, Vladimir Michailovich Ulyanov, Paul Underwood, Thomas Wolter.
Prp found by Jason Earls (and later Thomas Wolter, see below).
Konyagin-Pomerance primality proof by David Broadhurst.

The prime is in Prime Curios!

Update August 9 2005: Thomas Wolter found a second prp on the same form.
David Broadhurst again completed a Konyagin-Pomerance primality proof. It contains the decimal expansion. The picture part and known N+1 factors are the same.

Page made by Jens Kruse Andersen, jens.k.a@get2net.dk   home
Last updated August 9 2005.