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:

http://www.primenumbers.net/prptop/topdisc.php
and would have increased the world's stockpile of gigantic PRPs by 14%.

But alas, they are all provable.

-Mike Oakes