Published public keys could then be compared to this list and the prime factors would be known immediately with a simple database look-up. Mathematician: Let’s say we are working with all prime numbers that are about d digits long or shorter. The number of prime numbers less than this (applying the prime number theorem) is about which is approximately equal to . 56 mod 7 = (52)3 mod 7 = (25)3 mod 7 = (21+4)3 mod 7 = (4)3 mod 7 = 64 mod 7 = 63+1 mod 7 = 1. 311 mod 12 = 38+3 mod 12 = ((32)2)233 mod 12 = (92)227 mod 12 = (81)2(24+3) mod 12 = (72+9)23 mod 12 = (9)23 mod 12 = 81 x 3 mod 12 = (72+9)3 mod 12 = 9 x 3 mod 12 = 27 mod 12 = 3 ≠ 1.

When you want to outsmart the world, you turn to the facts. And the facts are in the science.