- Dec 1, 2004I have a 2004 addition for CPAP-4 (yes, it was very easy to find)

78006074.883#+k*2004+R is prime for k = [0...3]

Using the special crafted R of:

R=2114567933911681280472790383441990479992379628560566796354424357\

838755083647935493830969086740559072320624021043028003098506771578\

705193556075446873904579965613995564655278439586807781631424628487\

465675366956065147973222327951284073363128838151633809148759244135\

745954589064984106465530727879107072157718030628641179072983310965\

3930842047229740770849707899029657847082299

This is 379 decimal digit CPAP-4 with d=2004 (d chosen for the

year of finding).

Jim Fougeron.

--- In primenumbers@yahoogroups.com, "Jens Kruse Andersen"

<jens.k.a@g...> wrote:> In September Hans Rosenthal reported a prp CPAP-3 with large

difference in

> http://groups.yahoo.com/group/primeform/message/4700 :

that has

>

> > d=17676

> > is the largest known common difference for any CPAP-k (k > 2)

> > ever been discovered, as far as I know.

largest known

>

> Such records should be listed somewhere...

> The Largest Known CPAP's has today added a record table with the

> CPAP-k difference for each k:

on*, no

> http://hjem.get2net.dk/jka/math/cpap.htm#difference

>

> Hans daringly continued:

> > I dare to conjecture that within one year from now (5 Sep 2004)

> > one will find a larger value of d for any CPAP-k. Note that the

average

> > prime gap length for the form 9337#+k by testing k from 1 to

840000001

> > is 9717.

until now.

>

> Some people who know me may be surprised this conjecture has lasted

> Maybe Hans was challenging me - or maybe I just have illusions

about the world

> of prime constellations revolving around me :-)

Alm & Jens

> Anyway, I did not work on it until this month.

>

> New difference records have been set for CPAP-3 to -7 by Torbjörn

> Kruse Andersen.

record.

>

> k=3: p2506 + 21102n, n=0..2, Alm & Andersen

>

> Hans' 4003-digit prp CPAP-3 is unproven so it was not official

>

guarantee many

> k=4: Same as k=5 (a poor record for CPAP-4)

>

> k=5: p272 + 1350n, n=0..4, Andersen

>

> k=6: p218 + 840n, n=0..5, Alm & Andersen

>

> k=7: p133 + 420n, n=0..6, Alm & Andersen

>

> pN is an N-digit prime with no simple expression, chosen to

> composites. The decimal expansions are at the record page.

3,5,7).

> PrimeForm/GW prp'ed for the CPAP-3, the GMP library for the others.

> Marcel Martin's Primo proved all primes.

>

> The difference in a CPAP-k must be a multiple of k# (except CPAP-3

> p133 + 420n is the first known CPAP-k with non-minimal difference

for k > 6.

> Only difference 7# = 210 is known for CPAP-8, -9 and -10.

listed

> In fact, only one CPAP-10 is known at all. The discoverers get 4

> records for the price of 1: Longest CPAP, largest CPAP-10, smallest

CPAP-10,

> largest CPAP-10 difference.

guarantee many

>

> The record for k=4 is currently very easy with an algorithm to

> composites. It was found in the search for k=5.

>

> --

> Jens Kruse Andersen - << Previous post in topic Next post in topic >>