- The first known gigantic case of 3 consecutive primes in

arithmetic progression:

19067408*2^33333-12539 + 6270*n, for n = 0, 1, 2

In 2007 it was found to be a prp CPAP-3 by Jens Kruse Andersen,

Ken Davis, NewPGen, PrimeForm:

http://groups.yahoo.com/neo/groups/primeform/conversations/topics/8817

The last prime was easily provable. Two 10042-digit prp's have

now been proved by Pierre Cami with Primo. Certificates:

http://physics.open.ac.uk/~dbroadhu/cert/cpap10042a.zip

http://physics.open.ac.uk/~dbroadhu/cert/cpap10042b.zip

They took around 5 days each. PC's and Primo have improved since 2007.

The proven record had remained at 7535 digits since 2005. Recently it

was improved slightly 3 times without increasing the digit count:

http://users.cybercity.dk/~dsl522332/math/cpap.htm#k3

Now there are no prp CPAP-3's interfering with the proven top-10.

--

Jens Kruse Andersen I give here the details of my works to found this 7557 digits CPAP3

During the certifications of the gigantic CPAP3 of Jens I try to

understand how to found by myself ( if possible ) a way of finding

CPAP's.

I use PFGW & SCRIPTIFY to found the CPAP3 of the form k*2^n-1

+-g +-2*g for n =1 to 500 or more for the smallest k.

Sequences in EOIS A228452, A228454 and others in publication.

I found that in average the ratio k/n^1.75 is about 1.8

I try to found such CPAP3 in the range 7500 to 7600 digits and I see

that n need to be >=25000.

I born the 25 of july ,75 years ago so I choose n=25077 (25/07 and not 5 but 7 my lucky number)

I choose the range of 90000000 to 100000000 ( d'nt know why !!) for k and in less than 2 days I

was surprise to found 90568041*2^25077-9001 , -4501 PRP's as was -1 easely proved

prime with PFGW, the 2 others PRP's was certified with PRIMO in 4 days.

I d'nt use any sieve program , only SCRIPT and PFGW64 -f -e200000 test.txt

Here is all the story !

So thanks for David to help me to understand and use PFGW and SCRIPTIFY ,

thanks to Jens to give me the oportunity to be interested in CPAP's , thanks to you

and all friends there , and THANKS to 25 07 7 !!!

Now I am trying to work on CPAP3 of the form 2^n+k,+k+g,+k+2*g and here

I use the APTREEsieve program of Jens with n=35000 .

May be a result in a few days , months or years or never

> Message du 12/11/13 21:14

> De : paulunderwood@...

> A : primeform@yahoogroups.com

> Copie à :

> Objet : [primeform] RE: RE: RE: RE: Gigantic CPAP-3

>

>>

>

>

> ---In primeform@yahoogroups.com, wrote:

>

>>

>

>---In primeform@yahoogroups.com, wrote:

>

>> Now the 2 first primes are PRIMO certified , I put the numbers

> on the Prime Pages as CPAP3 but d'nt know how to put the PRIMO certificates.

> Thanks for your help

> Amitiés

> Pierre

>

>Pierre, congratulations, but you should have accredited PFGW (and any publically available sieve and any finders of the PRP CPAP) with the prover code.

>Good luck with finding a home for the certificates,

>Paul

>On second thoughts: In such cases, I see David, for example, uses two prover codes; one for PFGW and one for Primo,

>Paul

>

>

>---In primeform@yahoogroups.com, wrote:

>

>> There are now 3 CPAP with the last 90568041*2^25077-1 easely proved

> prime with PFGW and 90568041*2^25077-9001, 90568041*2^25077-4501

> as PRP's , but they are going to be certified with primo this week.

> Please David can you give me the way to store the ziped certificates

> when done ( I loose your Email adress to do this) ?

> Amitiés

> Pierre

>

>---In primeform@yahoogroups.com, wrote:

>

>The first known gigantic case of 3 consecutive primes in

> arithmetic progression:

> 19067408*2^33333-12539 + 6270*n, for n = 0, 1, 2

>

> In 2007 it was found to be a prp CPAP-3 by Jens Kruse Andersen,

> Ken Davis, NewPGen, PrimeForm:

> http://groups.yahoo.com/neo/groups/primeform/conversations/topics/8817

>

> The last prime was easily provable. Two 10042-digit prp's have

> now been proved by Pierre Cami with Primo. Certificates:

> http://physics.open.ac.uk/~dbroadhu/cert/cpap10042a.zip

> http://physics.open.ac.uk/~dbroadhu/cert/cpap10042b.zip

> They took around 5 days each. PC's and Primo have improved since 2007.

>

> The proven record had remained at 7535 digits since 2005. Recently it

> was improved slightly 3 times without increasing the digit count:

> http://users.cybercity.dk/~dsl522332/math/cpap.htm#k3

> Now there are no prp CPAP-3's interfering with the proven top-10.

>

> --

> Jens Kruse Andersen