# Zero Sink

## Monday, August 24, 2009

### Help Prove This Number Prime [Update: It's Done]

This number is a probable prime:
(10^127590)+((9*(10^42997)-2)/11)*(10^42297)+1
If written out, it is 127591 digits long and (in base 10) is a palindrome, reading the same forwards and backwards. It is also tetradic, meaning that it is a palindrome made up entirely of 0's, 1's, and 8's and therefore reads the same upside down, rotated 180 degrees, or in mirror image.

It would be nice to prove this number prime. It would be is one of the 20 largest known palindromic primes, and would be the 2nd largest known tetradic palindromic prime.

N-1 has these known factors:
2^42298*3^2*5^42297*7*5261*8803*98337713
N+1 has these known factors:
2*11*143666053607*801559942927

The cofactors aren't weren't quite sufficient to complete the proof with PFGW. I'm running curves with GMP-ECM to try to find more.

Primality testing ((10^127590)+((9*(10^42997)-2)/11)*(10^42297)+1) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Prime_Testing_Warning, unused factor from helper file: 19
Running N-1 test using base 11
Generic modular reduction using generic reduction FFT length 48K on A 423845-bit number
Running N-1 test using base 13
Generic modular reduction using generic reduction FFT length 48K on A 423845-bit number
Running N+1 test using discriminant 23, base 1+sqrt(23)
Generic modular reduction using generic reduction FFT length 48K on A 423845-bit number
Calling N-1 BLS with factored part 33.16% and helper 0.02% (99.51% proof)
((10^127590)+((9*(10^42997)-2)/11)*(10^42297)+1) is Fermat and Lucas PRP! (7041.5501s+0.0171s)

Update: Dr. Broadhurst came up with a KP proof.