- 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 "+30" and "+60" decades have triplets (in the decadal sense 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? - woodhodgson wrote:
> The set {11,13,17,19, 41,43,47, 71,73,79, 101,103,107,109}

There are only 2 admissible patterns, the above and its mirror

> shows two sets of quadruplets 90 apart, and the intervening

> "+30" and "+60" decades have triplets (in the decadal sense

> 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?

{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

http://tech.groups.yahoo.com/group/primenumbers/message/18318:

300000224101777931 + n,

for n in {0,2,6,8, 90,92,96,98, 180,182,186,188, 210,212,216,218}

--

Jens Kruse Andersen - Thank you Jens, also to Maximilian for his replies. It certainly confirms a long gap to the next occurrences. No doubt these should occur infinitely often according to general conjectures.

--- In primenumbers@yahoogroups.com, "Jens Kruse Andersen" wrote:

>

> 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

> > "+30" and "+60" decades have triplets (in the decadal sense

> > 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

> http://tech.groups.yahoo.com/group/primenumbers/message/18318:

> 300000224101777931 + n,

> for n in {0,2,6,8, 90,92,96,98, 180,182,186,188, 210,212,216,218}

>

> --

> Jens Kruse Andersen

>