Show that all sums of two consecutive odd prime
numbers have at least three prime factors, not necessarily distinct.
Example: 3+5=8. 8's factors: 2,2,2.
let p,q be consecutive prime numbers with 2<p<q
now since p,q are both prime then we have
p+q=2n thus 2 is a prime factor of their sum
n=(p+q)/2 thus
p<n<q
however, since p,q are consecutive primes then n is composite and thus has at least 2 prime factors. Thus p+q has at least 3 prime factors.

Posted by Daniel
on 20150205 15:11:27 