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