Twin primes: Difference between revisions

Revision as of 18:35, 20 April 2009

The term twin primes is used for a pair of odd prime numbers that differ by two. In other words, primes $p, p + 2$ are termed twin primes.

The twin primes conjecture states that there are infinitely many twin primes.

Cousin primes are two primes that differ by $4$ . Note that for $p > 3$ , if both $p$ and $p + 4$ are prime, $p + 2$ is not prime.
Sexy primes are two primes that differ by $6$ (and with no prime in between).

Prime quadruplet is a collection of four primes $p, p + 2, p + 6, p + 8$ .
Prime constellation is a sequence of consecutive primes $p_{1} < p_{2} < \dots < p_{k}$ for which the difference between the first and last prime is the least possible based on considerations of modular arithmetic relative to smaller primes.

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 The [[twin primes conjecture]] states that there are infinitely many twin primes.
+==Relation with other properties==
+===Related properties for pairs of primes===
+* [[Cousin primes]] are two primes that differ by <math>4</math>. Note that for <math>p > 3</math>, if both <math>p</math> and <math>p + 4</math> are prime, <math>p+2</math> is not prime.
+* [[Sexy primes]] are two primes that differ by <math>6</math> (and with no prime in between).
+===Related properties for more than two primes===
+* [[Prime quadruplet]] is a collection of four primes <math>p,p+2,p+6,p+8</math>.
+* [[Prime constellation]] is a sequence of consecutive primes <math>p_1 < p_2 < \dots < p_k</math> for which the difference between the first and last prime is the least possible based on considerations of modular arithmetic relative to smaller primes.