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• 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
Message 1 of 3 , Feb 10, 2013
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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
Message 2 of 3 , 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
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
Message 3 of 3 , Feb 11, 2013
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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