Quote:
Originally Posted by PawnProver44
Likewise, there should be infinitely many primes q such that 15*q4, 15*q2, 15*q+2, 15*q+4, are all prime. Still don't know how to prove this.

well a possible start would be to show all the cases possible
q=2,3,6x1,6x+1 and what each is equivalent to.
case q=2:
all parts are even so the result would be even so q=2 fails to meet the requirements
q=3:
produces 49 for the last one so q=3 is out.
q=6x1:
produces : 90x19, 90x17,90x13,90x11
q=6x+1
produces: 90x+11,90x+13,90x+17,90x+19
now you need to show that for any x values that these are all prime create primes 6x+1 or 6x1 or both infinitely often. x must already be of a certain form for 6x1 or 6x+1 to be composite so prove infinitely often that these forms are not met ?