Difference between revisions of "Prime triplet"

(New page: == Prime Triplet == Three consecutive prime numbers with a difference of two is called '''Prime Triplet'''. Eg:- 3,5,7.)
 
(Prime Triplet)
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Eg:- 3,5,7.
 
Eg:- 3,5,7.
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3,5,7 turns out to be the only prime triplet. This is because any set {n,n+2,n+4} mod 3 becomes {0,2,1},{2,1,0}, or {1,0,2}. Therefore in every triplet there exists one number that is divisible by 3. The only prime number divisible by 3 is 3 itself, so the only triplets possible are {1,3,5} and {3,5,7}. Since 1 is not a prime, {3,5,7} is the only prime triplet.

Revision as of 15:28, 20 December 2008

Prime Triplet

Three consecutive prime numbers with a difference of two is called Prime Triplet.

Eg:- 3,5,7.

3,5,7 turns out to be the only prime triplet. This is because any set {n,n+2,n+4} mod 3 becomes {0,2,1},{2,1,0}, or {1,0,2}. Therefore in every triplet there exists one number that is divisible by 3. The only prime number divisible by 3 is 3 itself, so the only triplets possible are {1,3,5} and {3,5,7}. Since 1 is not a prime, {3,5,7} is the only prime triplet.

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