Determine all pairs of prime numbers p and q less than 100, such that the following five numbers:

p+6, p+10, q+4, q+10, p+q+1

are all prime numbers.

(In reply to Solution by Brian Smith)

It is also possible that p=97, giving the numbers p+q+1=101, p+6=103, p+10=107. The problem only said that p and q are under 100, not necessarily that the other numbers are under 100. Therefore, the solutions are (7, 3), (13, 3), (37, 3), and (97, 3).

Posted by Math Man on 2024-07-01 17:25:50