[seqfan] Question on primes

[Creighton Kenneth Dement]

Dear Seqfans,

I have a quick question that is probably either trivial or really hard.

Observe that (2 + 1)(13 - 1) = 36 is a square. 2 and 13 are primes, but
they are not consecutive (i.e. there are other primes inbetween).

If p and q are consecutive primes, do we have

(p + 1)*(q - 1) is a square if and only if q = p + 2, i.e. p and q are
twin primes?

Sincerely,
Creighton