New AP 23 record.
- Man, I should pay more attention next
time. This AP 23 I found on June 24th 2006
is actually the new record. It ends with
1,195,284,944,428,129 and the old one
56211383760397 + 199678·23#·n ) ends with 1,036,239,621,869,317
There is also this one I found last
year 654737613204229 + 110135*23#*n n=0..22
At 01:14 PM 1/3/2007, Paul Underwood wrote:
>--- In[Non-text portions of this message have been removed]
>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
> > The above progression was meant to improve the smallest known
> > 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:
- Markus Frind wrote:
> Man, I should pay more attention nextCongratulations on improving your own AP23.
> time. This AP 23 I found on June 24th 2006
> is actually the new record. It ends with
> 1,195,284,944,428,129 and the old one
> 56211383760397 + 199678·23#·n ) ends with 1,036,239,621,869,317
> There is also this one I found last
> year 654737613204229 + 110135*23#*n n=0..22
http://hjem.get2net.dk/jka/math/aprecords.htm#news is updated with a
comment about discovery date.
But if somebody should suddenly claim they long ago found an
unpublished AP record which is no longer record, then don't expect a
place in the record history.
Gennady Gusev submitted an interesting AP18 today:
47 + 19622534420177523*17#*n, n=0..17
It greatly reduced the smallest known AP18 start from his own
602521111 + 189175*17#*n, n=0..17
but it's also the largest known AP18 (which is measured by ending
prime). Wroblewski's former AP18 record only lasted 3 days and looked
970080760458011996047 + 53#*n, n=0..17
Jens Kruse Andersen