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Searching for Prime Sextuplets with JavaScript

Doing Math with JavaScript
*Prime sextuplets* (or *prime 6-tuples*)
are sets of six primes {*p* – 4, *p*, *p* + 2, *p* + 6, *p* + 8, *p* + 12}
that form the *closest admissible 6-prime constellation*.
(An admissible prime constellation is an arrangement of primes that can occur infinitely many times.
Many arrangements are not admissible because of divisibility considerations; for example,
a set of six consecutive odd integers is not admissible because two of them must be divisible by 3.)
Examples of prime sextuplets are {7, 11, 13, 17, 19, 23},
{97, 101, 103, 107, 109, 113}, {16057, 16061, 16063, 16067, 16069, 16073}, or
{19417, 19421, 19423, 19427, 19429, 19433}.
One can prove that each prime sextuplet has the form
{30*x* + 7, 30*x* + 11, 30*x* + 13,
30*x* + 17, 30*x* + 19, 30*x* + 23} for a certain integer *x*.
Our definition implies that the *width* of a prime sextuplet is 16; it also implies that three
consecutive odd numbers {3, 5, 7} cannot be part of a sextuplet.
(Therefore, the sets of six primes
{2,3,5,7,11,13},
{3,5,7,11,13,17}, and
{5,7,11,13,17,19}
are *not* prime sextuplets by our definition.
These arrangements of primes are *not* admissible
and do *not* have the form 30*x* + 7, ..., 30*x* + 23 described above.)

Click the **Run** button to find prime sextuplets by calling the `nextPrime6tupleMR_('n')`

in the left column:

**See also:**

• Twin primes

• Prime quadruplets

• Maximal gaps between prime *k*-tuples

Doing Math with JavaScript.
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