Difference between revisions of "Prime triplet"
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== Prime Triplet == | == Prime Triplet == | ||
| − | Three consecutive [[Prime|prime]] numbers with a difference of two is called '''Prime Triplet'''. | + | Three consecutive [[Prime number|prime]] numbers with a difference of two is called '''Prime Triplet'''. |
Eg:- 3,5,7. | 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. | 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 16:31, 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.
