> 63734273908111 + 11*19#*n, n=0..18

Now I got even a smaller difference:

20736372344841161 + 5*19#*n, n=0..19

Note that this is an AP20.

Thanks for the info about 4th AP23, Paul.

Jarek- --- In primeform@yahoogroups.com, "jarek372000" <jwr@...> wrote:

> 20736372344841161 + 5*19#*n, n=0..19

Impressive work, Jarek!

I hope all your 74 machines have good cooling fans.

Jak zyczyc ogolnie szczescia!

David - There is also this one I found last year 654737613204229 +

110135*23#*n n=0..22

Markus.

At 01:14 PM 1/3/2007, Paul Underwood wrote:

>--- In

[Non-text portions of this message have been removed]

><mailto:primeform%40yahoogroups.com>primeform@yahoogroups.com,

>Jaroslaw Wroblewski <jwr@...> wrote:

> >

> > > > 63734273908111 + 11*19#*n, n=0..18

> > >

> > > Jens recognizes 23*19# as a

> > > "valid AP19 difference for simultaneous primes",

> > > but does /not/ recognize 11*19#.

> >

> > Once Jens has decided to allow AP-k with predetermined difference as

> > simultaneous primes and once he decided to allow a set of 3 valid

> > differences, the choice he made seems more natural to me than,

> > say, k#, 2*k# and 3*k#. But of course this is a matter of personal

>taste.

> >

> > The above progression was meant to improve the smallest known

>difference,

> > which was at 155*19# until now.

> >

> > BTW, what is the complete list of known AP23? From Jens's website,

> > including news section, I was able to trace 3 AP23's. Are there any

> > more? Perhaps it would be a good idea to keep track of all known AP23,

> > not only those best in one of the rankings.

> >

>

>There are four I know of -- but I am asking Markus if he has any more:

><http://www.primepuzzles.net/puzzles/puzz_268.htm>http://www.primepuzzles.net/puzzles/puzz_268.htm

>

>Paul

>

>

>