The majority of the decimal expansion of this PRP has the pattern:
13579864201357986420...

PFGW Version 1.2.0 for Windows [FFT v23.8]

Primality testing 1357986420*(10^(10*1001)-1)/(10^10-1)+4637
[N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Running N+1 test using discriminant 7, base 2+sqrt(7)
1357986420*(10^(10*1001)-1)/(10^10-1)+4637 is Fermat and Lucas PRP!

To be completed...