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Old 2022-04-17, 17:28   #1
Stargate38's Avatar
"Daniel Jackson"
May 2011

739 Posts
Default Primes p such that p^2+p+1=q is prime, and p is largest prime factor of q^3-1

I was wondering if there's even such a prime p that fits the following:

1. p^2+p+1=q is prime (seems that p must be of the form 6n-1, other than 2 and 3).
2. Largest prime factor of q^3-1 is p.

So far, I haven't found any that fit #2 (searched up to p=997), but I'm guessing #1 has infinitely many solutions. Anyone know how I might do this in PARI/gp? I want to search up to at least p=9999991.
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