613 is an amusing prime curio: it s prime, then rotating the first digit to the back to get 136 produces a triangular number, (16*17)/2 = 136; and rotating the first digit of that number to the end gives the square, 361 = 19^2.

PFGW Version 1.2.0 for Windows [FFT v23.8]

Primality testing 2^126006+613
[N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 4+sqrt(5)
Running N+1 test using discriminant 5, base 5+sqrt(5)
Running N+1 test using discriminant 5, base 6+sqrt(5)
2^126006+613 is Fermat and Lucas PRP!

To be completed...