## 1931 4241 6551 8861 11171

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• A cursory glance at some prime numbers the other day, came up with the following sequence 1931 4241 6551 8861 11171 5 primes in arithmetic progression
Message 1 of 3 , Jul 7, 2009
A cursory glance at some prime numbers the other day, came up with the following sequence

1931 4241 6551 8861 11171

5 primes in arithmetic progression separated by 2310. Not very remarkable in itself, except that each of these primes is a twin prime.

Which leads me to wonder what is the longest known sequence of twin primes in an arithmetic progression?

Can anyone guide me on this?

Bob

[Non-text portions of this message have been removed]
• ... well, it does not seem surprising since 2310 is 11# or if you want 11*7*5*3*2. If x+11# has a given gap, there is a good chance that x+(y+11#) has the same
Message 2 of 3 , Jul 7, 2009
Bob Gilson wrote:
> A cursory glance at some prime numbers the other day, came up with the following sequence
> 1931 4241 6551 8861 11171
> 5 primes in arithmetic progression separated by 2310.
> Not very remarkable in itself, except that each of these primes is a twin prime.

well, it does not seem surprising since 2310 is 11#
or if you want 11*7*5*3*2. If x+11# has a given gap, there
is a good chance that x+(y+11#) has the same gap for some y.
It's all about wheel sieves ;-)

> Which leads me to wonder what is the longest known sequence of twin primes in an arithmetic progression?

If twin primes are infinite (which i don't doubt),
then there can be arbitrarily long sequences of the above form,
but with a higher primorial than 11#.

> Can anyone guide me on this?

Hope I helped.

What is interesting to me is how the gap is "closed",
that is : given a prime p, what is the formulat that
finds the maximum y where x+(y*p#) becomes composite
for all the valid x.

regards,

> Bob
yg
• ... http://www.primepuzzles.net/puzzles/puzz_121.htm shows: 302296020 + 153363210*n +/- 1, for n=0..9 -- Jens Kruse Andersen
Message 3 of 3 , Jul 7, 2009
Bob Gilson wrote:
> Which leads me to wonder what is the longest known sequence of twin primes
> in an arithmetic progression?

http://www.primepuzzles.net/puzzles/puzz_121.htm shows:
302296020 + 153363210*n +/- 1, for n=0..9

--
Jens Kruse Andersen
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