Whether twin primes satisfy this one? It seems that difference of squares of any twin primes $+1$ will always lead to number which might be a) A square of a twin prime b) Itself a twin prime $C$ = ($A^2$-$B^2$ )+$1$ ------> $(1)$ Where $C$ --- > might be a twin prime or square of a twin prime, $A$ and $B$ are twin primes where $A$ is > $B$ My questions is whether eqn ($1$) is true?

If $A$, $B$ are twin primes, they differ by 2, so the conjecture seems to be that

> if $C = 2(A + B) + 1$, with $A$, $B$ twin primes, then $C$ is either a twin prime or square of a twin prime.

That's quickly falsified by taking $A = 101, B = 103$. For then $C = 409$ which is neither a twin prime nor the square of one.