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.

(In reply to Odd premise (spoiler) by Steve Herman)

I think this was meant to apply to consecutive primes, restricting to odd primes to account for the oddball 2+3=5.  I can't come up with a complete proof but checking the first 10,000 primes confirms this is true at least that far out so I'm suspecting that a deeper number theory analysis could prove it true for all consecutive primes (excluding 2+3).

Posted by Daniel on 2015-02-05 14:46:07