About 1 in 700 1024-bit numbers is prime. There are 1023512 Hamming-distance 2 numbers for a 1024-bit number, about 750 of them will be prime.

If you found no Hamming distance 1 primes (expected: 0.68) and 3-400 Hamming distance 2 primes (expected: 750), this is one really* bad "prime"...