perplexus.info :: Just Math : Consecutive Primes

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.

Comments: ( You must be logged in to post comments.)

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

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