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• Feb 11, 2013
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woodhodgson wrote:
> The set {11,13,17,19, 41,43,47, 71,73,79, 101,103,107,109}
> shows two sets of quadruplets 90 apart, and the intervening
> that I use the term, not necessarily ones with a minimal
> span of 6).
>
> Does anyone have a list of the next few occurrences of this pattern?

There are only 2 admissible patterns, the above and its mirror
{11,13,17,19, 41,47,49, 73,77,79, 101,103,107,109}

A search found 10 occurrences in total below 10^17.
2 of them are the mirror pattern.
The first prime and the number of other primes in the interval:

11, 11 other primes
549758002658141, 2 other primes
1444747726722731, 1 other prime
4869691549793501, 2 other primes
7973040075706331 (mirror pattern), 1 other prime
21603285535472981, 0 other primes
21859392938284241, 1 other prime
23490659029317911, 0 other primes
28423532235584111 (mirror pattern), 1 other prime
94859808174585731, 0 other primes

The first case of 4 prime quadruplets as closely together as admissible is in