Is $1000000000000066600000000000001$ (Belphegor's prime) actually a prime? There is a Wikipedia article about that evil Belphegor's prime, but the references there seem relatively weak. Is this number actually a prime?
 A: As far as I know, Pari/GP offers a deterministic primality test (contrary to the probability test of Mathematica).
                            GP/PARI CALCULATOR Version 2.7.3 (released)
                    i386 running darwin (x86-64/GMP-6.0.0 kernel) 64-bit version
       compiled: May 24 2015, Apple LLVM version 6.0 (clang-600.0.57) (based on LLVM 3.5svn)
                                      threading engine: single
                           (readline v6.3 enabled, extended help enabled)

                               Copyright (C) 2000-2015 The PARI Group

PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY 
WHATSOEVER.

Type ? for help, \q to quit.
Type ?12 for how to get moral (and possibly technical) support.

parisize = 8000000, primelimit = 500000
? isprime(1000000000000066600000000000001)
%1 = 1

This is confirmed by http://sti15.com/nt/primality.cgi where, choosing “Proof”, we get

Proving... output indicates progress. Certificate and timing at end.
  $1000000000000066600000000000001$ is DEFINITELY PRIME.
  Time taken: $0.523$ milliseconds.
[MPU - Primality Certificate]
Version 1.0

Proof for:
N 1000000000000066600000000000001

Type BLS5
N  1000000000000066600000000000001
Q[1]  5
A[0]  3
----


(Thanks to DanaJ for suggesting the site for the certificated primality test.)
A: Both Mathematica and WolframAlfa confirm that this number is prime:
In[42]:= PrimeQ[1000000000000066600000000000001]

Out[42]= True

