PRP 15424 (show) (3075^4489-1)/(3075^67-1)<15424> = 1782875975...01<15424>

PRP 10100 (show) (894^3481-1)/(894^59-1)<10100> = 2999088763...81<10100>

PRP 10107 (show) (898^3481-1)/(898^59-1)<10107> = 1293076072...77<10107>

PRP 2623 (show) (1696^841-1)/(1696^29-1)<2623> = 1966928221...09<2623>

@Peter Good question. I'll think about it. We had a similar discussion about Fermat Primes in simplifire's chatroom. I tend to say that the Mersenne Primes are infinite.

@Peter It seems that $59$ is a frequent prime here. Occured for bases 2, 75, 894, 898.

PRP 14746 (show) (10688^3721-1)/(10688^61-1)<14746> = 5767520955...01<14746>

@MartinHopf $61$ is now a "good" prime !