Prime triplet

Revision as of 00:59, 17 March 2009 by Chenhsi (talk | contribs) (Discussion)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

A set of three prime numbers which form an arithmetic sequence with common difference two is called a prime triplet.


An example of a prime triplet is $\{3,5,7\}$.

$\{3,5,7\}$ turns out to be the only prime triplet. This is because any set $\{n,n+2,n+4\} \pmod 3$ 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.

See Also