## An 85-digit AP13

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• Immediately after Ken announced his 83-digit AP13s in May: http://tech.groups.yahoo.com/group/primeform/message/10310 I resolved to continue our game of AP-k
Message 1 of 3 , Dec 22, 2010
Immediately after Ken announced his 83-digit AP13s in May:
http://tech.groups.yahoo.com/group/primeform/message/10310
I resolved to continue our game of AP-k leapfrog and retake the record.

But it has been an uphill struggle.
I spent 255 GHz-days failing to find one at 101 digits, and had to start over, with a more modest target.

Finally, an AP13 with 85 digits turned up today:-

(1296982250+14976848*n)*191#+1 is prime for n=0..12

All confirmed prime with PFGW -tc

Input/output statistics:-
Numbers tested by NewPGen: 2*10^9
NewPGen reduced these (by sieving to depth 150 billion) to: 4.1*10^8
PRP's found by PFGW: 98 million
AP12's found: 25
AP13's found: 1

Run-time statistics:-
NewPGen: 8 GHz-hrs
PFGW: 63 GHz-hrs
Pascal program to find AP's: 331 GHz-days

Poisson was clearly saving this up for Christmas: about 15 AP12's should have been enough to yield an AP13.

Mike
• ... Congratulations! http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated. -- Jens Kruse Andersen
Message 2 of 3 , Dec 22, 2010
Mike Oakes wrote:
> (1296982250+14976848*n)*191#+1 is prime for n=0..12

Congratulations!
http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated.

--
Jens Kruse Andersen
• ... 101 digits was indeed ambitious. ... Congratulations. Looks like I have a new challenge for 2011. Though I hope to be spending a fair bit of resources
Message 3 of 3 , Dec 23, 2010
--- In primeform@yahoogroups.com, "mikeoakes2" <mikeoakes2@...> wrote:
>
> Immediately after Ken announced his 83-digit AP13s in May:
> http://tech.groups.yahoo.com/group/primeform/message/10310
> I resolved to continue our game of AP-k leapfrog and retake the record.
>
> But it has been an uphill struggle.
> I spent 255 GHz-days failing to find one at 101 digits, and had to start over, with a more modest target.
101 digits was indeed ambitious.
>
> Finally, an AP13 with 85 digits turned up today:-
>
> (1296982250+14976848*n)*191#+1 is prime for n=0..12
>
> All confirmed prime with PFGW -tc
>
> Input/output statistics:-
> Numbers tested by NewPGen: 2*10^9
> NewPGen reduced these (by sieving to depth 150 billion) to: 4.1*10^8
> PRP's found by PFGW: 98 million
> AP12's found: 25
> AP13's found: 1
>
> Run-time statistics:-
> NewPGen: 8 GHz-hrs
> PFGW: 63 GHz-hrs
> Pascal program to find AP's: 331 GHz-days
>
> Poisson was clearly saving this up for Christmas: about 15 AP12's should have been enough to yield an AP13.
Congratulations.
Looks like I have a new challenge for 2011.
Though I hope to be spending a fair bit of resources particapting in the 1000 digit ap9 search.
It also saves me working out which of the 16 83 digit ap13's I currently have is the largest.
Currently at
369 AP12's
16 AP13's
0 AP14's (you'll be among the first to know when I get lucky)
cheers
Ken
> Mike
>
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