Prime95: PRP-3
PFGW: Fermat and Lucas PRP
108604 mod 35 == 34, any 10^(35k+34)+7 is divisible by 71
108624 mod 95 == 19, any 10^(95k+19)+7 is divisible by 191
10^108624+7 has "algebraic" factors only

To be completed...