[seqfan] q, p, (q^p - p - q)/p and (p^q - p - q)/p are primes

[юрий герасимов]

Dear SeqFans, 
Easy read primes q such that both p and (q^p - p - q)/p is prime, but Magma software does not allow me to carry out complex calculations and therefore I ask for your help
 (for Primes p such that  both q and (q^p - p - q)/p is prime: if q = 2, then p = 5, 7, 349, 1123, ..., if q = 3, then p = 2, 3, 5, 7, 11, 37, 43, 953, ..., if q = 5, then p = 7, 11, 13, 
229, ..., if q = 7, then p = 5, 19, 67, ..., if q = 11, then p = 3, ..., if q = 13, then p = 3, 13, 227, 373, ..., if q = 17, then p = 53, 163, ...if q = 19, then p = 11, 67, ..., if q = 23, 
then p = 181, ... or for Semiprimes p*q such that both p^q - p - q and (q^p - p - q)*q/p is semiprime: 9, 33, 35, 111, 169, ...). Best regards. JSG