Prime Sextuplets with JavaScript

Searching for Prime Sextuplets 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 {30x + 7, 30x + 11, 30x + 13, 30x + 17, 30x + 19, 30x + 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 30x + 7, ..., 30x + 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