Primes p such that both p^2 + 2 and p^2 - 2 are semiprimes.
Discussion
Fri May 16
23:31
Michael B. Porter: Thank you, Charles.
Discussion
Thu May 15
01:18
Charles R Greathouse IV: If p > 3 is prime then p^2 = 1 mod 3 hence 3 | p^2 + 2.
Discussion
Fri May 09
22:56
Alonso del Arte: Is it possible for both (p^2 + 2) and (p^2 - 2) to be semiprime but neither be divisible by 3? Why or why not?
Sat May 10
02:55
K. D. Bajpai: If both (p^2+2) and (p^2-2) be semiprimes then in all the cases (p^2+2) is divisible by 3, but in no case (p^2-2) is divisible by 3. Explored up to p(20000).
12:52
Alonso del Arte: This is a step in the right direction. But you need to go further, though. How do you know that your assertion won't suddenly fail for p(20001)? p(20002)? p(20003)? A mathematical proof is needed.
