## Prime Sextuplets

Friday, November 28, 2014

A couple of days ago, the Riecoin project (a virtual currency and distributed computing platform) posted a press release announcing they have quietly broken the record for the largest prime number sextuplet:

A prime sextuplet consists of six prime numbers packed together as tightly as possible. For sextuplets, “as tightly as possible” means that the largest is 16 plus the smallest of the numbers.

The smallest prime sextuplet is {7, 11, 13, 17, 19, 23} and generally
they take the form of a prime number `N`

such that these six numbers are
all prime: {N+0, N+4, N+6, N+10, N+12, N+16}.

It’s kind of neat that you can use Factor to confirm their result:

```
USE: math.primes
689702036532655186685581028503873005405874329363269153979622096014346785019088707220301256048568366498602811964467654774670820091972463194208186476882699386082393716593309811371422836387527549653095824492750394092045532275098135652952423078356472379653908988713872759020566218763497459878106775183203857648413997381256598543877696056491021898353604500233203798629403923570165634119564742536549584121471881689569379964364152289494693118199337926886001843460903637314310532482306798517536171711379098711480663572269535063407688377687623951196977582998449120940358830276897328119483620011984713125859631603652231485340570118364685553782567043880668996080767
{ 0 4 6 10 12 16 } [ + ] with map [ prime? ] all? .
```

Factor uses an implementation of the probabilistic Miller-Rabin primality test in the math.primes.miller-rabin vocabulary, which on my laptop takes just over 3 seconds.