Unsure what specifically the gp was referring to but there is a known relation between L-functions and the prime number sequence, see Riemann hypothesis. And p

Unsure what specifically the gp was referring to but there is a known relation between L-functions and the prime number sequence, see Riemann hypothesis. And p-adics are constructed using modulo some prime. With all these prime relations maybe p-adic L-functions could lend themselves to any number of prime adjacent conjectures: distribution, twins, goldbach, Riemann.