Search (probable) primes of the form (a^p-b^p)/(a-b) and (a^p+b^p)/(a+b) with a>b>0 and gcd(a,b)=1 for odd prime p: (currently at n=42.9K)
(9,7): (N-) 3, 5, 7, 4703, 30113 (N+) 3, 107, 197, 2843, 3571, 4451, 31517, 44819
(10,7): (N-) 31, 103, 617, 10253, 10691, 35353 (N+) 3, 5, 11, 19, 1259, 1399, 2539, 2843, 5857, 10589
(11,6): (N-) 3, 11, 163, 191, 269, 1381, 1493, 38453 (N+) 5, 7, 107, 383, 17359, 21929, 26393
(11,7): (N-) 5, 19, 67, 107, 593, 757, 1801, 2243, 2383, 6043, 10181, 11383, 15629 (N+) 7, 1163, 4007, 10159
(11,8): (N-) 7, 11, 17, 37, 521, 877, 2423 (N+) 3, 13, 31, 59, 131, 223, 227, 1523
(11,9): (N-) 5, 31, 271, 929, 2789, 4153 (N+) 3, 17, 41, 43, 59, 83
(12,7): (N-) 3, 7, 13, 47, 89, 139, 523, 1051 (N+) 3, 7, 67, 79, 167, 953, 1493, 3389, 4871
All other (a,b) with a>b>0 and gcd(a,b)=1 and a<=12 have been searched by OEIS to at least n=100K.

To be completed...