Oops, looks like I made several mistakes in the above calculations. For a 768 bit number the primes would be 384 bits each, gaps between numbers of the form "2

Oops, looks like I made several mistakes in the above calculations. For a 768 bit number the primes would be 384 bits each, gaps between numbers of the form "27a^2 ..." would be 10^58 apart, and weak primes would be at worst one out of 10^56. Still extremely unlikely, but not by as much as I thought.