Prime-Generating Quadratics of form 2 a squared plus p

Theorem
The quadratic form:
 * $2 a^2 + p$

yields prime numbers for $a = 0, 1, \ldots, p - 1$ for values of $p$:
 * $3, 5, 11, 29$

29
When $x = p$ we have:

which has divisors $p$ and $2 p + 1$ and so is not prime.