>>13098089Every multiple of 2 is composite, therefore less than half of all natural numbers are prime.
Every multiple of 3 is composite, therefore less than a third of all natural numbers are prime.
Taken together, in any six consecutive natural numbers (6k to 6k+5), 6k, 6k+2, 6k+3, and 6k+4 will obviously be composite. This leaves 6k+1 and 6k+5. Thus, except for 2 and 3, every prime is expressible as 6k±1.
