All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Consecutive Primes (Posted on 2005-01-24)
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

 Submitted by David Shin Rating: 3.1667 (6 votes) Solution: (Hide) Let p and q be consecutive odd primes. Since p+q is even, we may immediately factor p+q = 2*((p+q)/2). Furthermore, since ((p+q)/2) is a number strictly between p and q, and since there are no primes between p and q, we know that ((p+q)/2) has at least two prime factors. This makes at least 3 total prime factors.

 Subject Author Date Some thoughts on a particular case K Sengupta 2007-05-11 13:02:14 i goofed Ady TZIDON 2005-01-24 19:54:49 re: at least 3 - WRONG e.g. 2005-01-24 16:16:49 re: at least 3 Tristan 2005-01-24 15:47:57 at least 3 Ady TZIDON 2005-01-24 15:14:59 Solution Old Original Oskar! 2005-01-24 13:56:19

 Search: Search body:
Forums (0)