The standard prime groups have their highest and lowest 64 bits set, and as many as possible of the rest taken from the binary expansion of pi.  The group #14 prime for example is<p>p = 2^2048 - 2^1984 - 1 + 2^64 * { [2^1918 pi] + 124476 }<p>The value 124476 is the smallest non-negative value which results in p and (p-1)&#x2F;2 both being prime and 2 being a quadratic residue mod p; this ensures that the subgroup {2^0, 2^1, 2^2, 2^3, ... } is cyclic.<p>We assume that the binary expansion of Pi is not selected maliciously. ;-)