### 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.

(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.

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

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.

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