- Here is a new AP4 record at 15004 digits:-

(1000362700+2571033*n)*34687#+1 is prime for n=0..3

All confirmed prime with PFGW -tc

Input/output statistics:-

Numbers tested by NewPGen: 10^7

NewPGen reduced these (by sieving to 1.8T) to: 3.7*10^6

Numbers tested by PFGW: 1.3*10^6

PRP's found by PFGW: 2051

AP3's found: 661

AP4's found: 0

One AP4 was found by extending all the AP3's upwards.

Run-time statistics:-

NewPGen: 56.5 GHz-days

PFGW: 457 GHz-days

Pascal program to find AP's: < 1 sec

Since the main bottleneck is the PFGW run, the Pascal program was run periodically to see what AP3's turned up, these being then extended upwards to look for an AP4.

A week ago, I tried a new trick (influenced by some of Ken's reported procedures):-

as about 1/3 of the NewPGen range had been PFGW'd, with 1805 PRPs found, I wrote a program to look through the 0.5*1805^2 AP2's and output the succeding AP3 term provided that both it and the following (AP4) term were in the not-yet processed region of the NewPGen-filtered candidates (and so each was about 3 times more likely than usual to be a PRP).

This gave 105,612 candidates, which took PFGW only about a week to process, yielding 162 new PRPs, each of which was guaranteed, by construction, to produce at least one new AP3. When these PRPs were added to those already found, the number of AP3's jumped from 429 to 661, a relatively huge increase for just one week's processing.

The trick (which could have been periodically repeated of course) paid off first time.

I offer it FOC to my competitors!

-Mike Oakes - --- In primeform@yahoogroups.com,

"mikeoakes2" <mikeoakes2@...> wrote:

> For comparison, I've checked what numbers my "hash"

I estimated the time for a Poisson mean of 1.0

> technology would require for a record of this size,

> for a "vanilla" detection algorithm

> Total: 15.818496 GHz-yrs

at about half of that, but I'm not telling

just how unlucky I was, in fact :-(

Please note that the cost of my big database of 25000-bit

primes is not included, since this had already been amortized

over several previous records, one going back to 2005:

http://primes.utm.edu/primes/page.php?id=73546

The key to my method was to recycle primes with only

31% of the digits of the largest member of the new AP4.

You can work out, from past CHG performance, how much

higher this recycling might take one :-)

> whether the AP3 record was about 10 times as burdensome?

Not for me, since here I merely stole the all the AP2s from

the public database :-)

David