# Prime Sextuplets

If {p-4, p, p+2, p+6, p+8, p+12} are primes then it becomes a prime sextuplet. Alternative defintion is {p, p+4, p+6, p+10, p+12, p+16}.

Our definition, all cases of primes {p-4, p, p+2, p+6, p+8, p+12}, follows from defining a prime sextuplet as the closest admissible constellation of six primes.

A prime sextuplet contains two close pairs of twin primes, a prime quadruplet, four overlapping prime triplets, and two overlapping prime quintuplets.

It is not known if there are infinitely many prime sextuplets. Once again, proving the twin prime conjecture might not necessarily prove that there are also infinitely many prime sextuplets. Also, proving that there are infinitely many prime quintuplets might not necessarily prove that there are infinitely many prime sextuplets.

In the digital currency riecoin one of the goals[3] is to find prime sextuplets for large prime numbers p using distributed computing.

First 5: {7, 11, 13, 17, 19, 23}, {97, 101, 103, 107, 109, 113}, {16057, 16061, 16063, 16067, 16069, 16073}, {19417, 19421, 19423, 19427, 19429, 19433}, {43777, 43781, 43783, 43787, 43789, 43793}

Checkout list of first: 10 prime sextuplets. You can also check all prime sextuplets.

## External#

- OEIS: A022008
- Wikipedia: Prime sextuplets

## Tags#

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