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Consecutive Primes (
Posted on 20050124
)
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
See The Solution
Submitted by
David Shin
Rating:
3.1667
(6 votes)
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Solution
 Comment 1 of 6
If P and Q are consecutive odd primes, then their average ½(P+Q) is integer, and not a prime since P<½(P+Q)<Q, so ½(P+Q)=MN, and then P+Q=2MN, as desired.
Posted by
Old Original Oskar!
on 20050124 13:56:19
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