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Some special sums (Posted on 2015-02-05) Difficulty: 2 of 5
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.

No Solution Yet Submitted by Ady TZIDON    
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solution | Comment 3 of 4 |
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 2015-02-05 15:11:27
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