Show that the sum of two consecutive odd primes has at least 3 (not necessarily distinct) prime factors. For example,

3+5=2*2*2
5+7=2*2*3
7+11=2*3*3

1 is not a prime number

let 1st odd prime be 2*n-1
then the 2nd 2*n+1


the sum is 4*n=2*2*n

q.e.d.

Posted by Ady TZIDON on 2005-01-24 15:14:59