It is a cofactor of (152^n-151^n)/(152-151).
For the smallest prime of the form (a^p-b^p)/(a-b) and (a^p+b^p)/(a+b) for coprime a, b, 1<=b<a<=50, odd prime p, some largest primes were found, the top 10 (probable) primes are: (sorted by exponent)
(48^58543-47^58543)/(48-47), (18^25667-1^25667)/(18-1)
(38^16747+7^16747)/(38+7), (37^13217-34^13217)/(37-34)
(47^9181+37^9181)/(47+37), (31^6961-6^6961)/(31-6)
(47^5641-23^5641)/(47-23), (40^5261-19^5261)/(40-19)
(43^3719+27^3719)/(43+27), (47^3671+46^3671)/(47+46)

There are 10 remaining families:
(a^p-b^p)/(a-b): (a,b)=(43,7), (46,31), (47,33), (49,46)
(a^p+b^p)/(a+b): (a,b)=(32,5), (44,43), (46,11), (49,46), (50,37), (50,43)

To be completed...