## A gigantic AP-4

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• Here is a new AP4 record at 10004 digits:- (2024725+197732*n)*23159#+1 is prime for n=0..3 All confirmed prime with PFGW -tc This displaces David s 7534-digit
Message 1 of 133 , Dec 16, 2006
Here is a new AP4 record at 10004 digits:-

(2024725+197732*n)*23159#+1 is prime for n=0..3

All confirmed prime with PFGW -tc

This displaces David's 7534-digit record which, having stood for nearly
2 years, was the 4th-longest surviving AP-n record, as Jens's page
shows:
http://hjem.get2net.dk/jka/math/aprecords.htm

Input/output statistics:-
Numbers tested by NewPGen: 3*10^6
NewPGen reduced these (by sieving to 0.3T) to: 1.18*10^6
Numbers tested by PFGW: 985451
PRP's found by PFGW: 1939
AP3's found: 690
AP4's found: 1

Run-time statistics:-
NewPGen: 13.5 GHz-days
PFGW: 340 GHz-days
Pascal program to find AP's: 2 GHz-secs

Poisson was slightly favourable: about 1200 AP3's (which would have
required about 1939*sqrt(1200/690)=2560 PRPs) was the expected number
needed to get an AP4.

1939 gigantic PRPs is quite a lot to have had to find: if they had
(only) been PRPs they would have pushed me to Rank 2 on Henri's page:
and would have increased the world's stockpile of gigantic PRPs by 14%.
But alas, they are all provable.

-Mike Oakes
• ... http://mat.fc.ul.pt/ind/ncpereira/Bounds%20for%20Th,Ps,Ga,Ri.pdf And some further excursions of the related function:
Message 133 of 133 , May 15, 2010
> Let puzzle(n) = sqrt(n)*(1 - log(n#)/n)
>
> Puzzle 1: Try to find a prime, p_min, such that
> puzzle(p_min) < puzzle(110102617)
>
> Puzzle 2: Try to find a prime, p_max, such that
> puzzle(p_max) > puzzle(19373)

http://mat.fc.ul.pt/ind/ncpereira/Bounds%20for%20Th,Ps,Ga,Ri.pdf

And some further excursions of the related function:
http://www.primefan.ru/stuff/primes/table.html
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