- --- In primeform@yahoogroups.com,

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

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

Here, eventually, is my reply:

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

Calling Brillhart-Lehmer-Selfridge with factored part 31.24%

3*164196977*2^80000-1631979959*2^25001-1 is Lucas PRP! (103.0930s+0.0038s)

Calling Brillhart-Lehmer-Selfridge with factored part 31.40%

164196977*2^80001-1631979959*2^25000-1 is Lucas PRP! (99.0570s+0.0044s)

Calling Brillhart-Lehmer-Selfridge with factored part 99.97%

164196977*2^80000-1 is prime! (30.1911s+0.0057s)

Calling Brillhart-Lehmer-Selfridge with factored part 99.88%

1631979959*2^25000-1 is prime! (2.4893s+0.0047s)

The two largest elements of this AP4, with 24092 and 24091 digits,

were proven prime using the method of Konyagin and Pomerance.

David Broadhurst, 24 October 2010 - David Broadhurst wrote:
> 3*164196977*2^80000-1631979959*2^25001-1 is Lucas PRP!

Congratulations on a large record improvement.

> 164196977*2^80001-1631979959*2^25000-1 is Lucas PRP!

> 164196977*2^80000-1 is prime!

> 1631979959*2^25000-1 is prime!

>

> The two largest elements of this AP4, with 24092 and 24091 digits,

> were proven prime using the method of Konyagin and Pomerance.

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

--

Jens Kruse Andersen - --- In primeform@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
>

David

> --- In primeform@yahoogroups.com,

> "mikeoakes2" <mikeoakes2@> wrote:

>

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

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

>

> Here, eventually, is my reply:

>

> Calling Brillhart-Lehmer-Selfridge with factored part 31.24%

> 3*164196977*2^80000-1631979959*2^25001-1 is Lucas PRP! (103.0930s+0.0038s)

>

> Calling Brillhart-Lehmer-Selfridge with factored part 31.40%

> 164196977*2^80001-1631979959*2^25000-1 is Lucas PRP! (99.0570s+0.0044s)

>

> Calling Brillhart-Lehmer-Selfridge with factored part 99.97%

> 164196977*2^80000-1 is prime! (30.1911s+0.0057s)

>

> Calling Brillhart-Lehmer-Selfridge with factored part 99.88%

> 1631979959*2^25000-1 is prime! (2.4893s+0.0047s)

>

> The two largest elements of this AP4, with 24092 and 24091 digits,

> were proven prime using the method of Konyagin and Pomerance.

Many congratulations on your big new record.

You don't say what effort was involved.

For comparison, I've checked what numbers my "hash" technology would require for a record of this size, for a "vanilla" detection algorithm, i.e. without any Ken-type extension tricks.

k=4 q=55793

M1=19890161. M2=39780323.

digits: 24094.885

score=80.718039

PRP'ing: 15.818496 GHz-yrs (100.00000%)

APk-detection: 0.000000012682880 GHz-yrs (0.000000080177533%)

Total: 15.818496 GHz-yrs

APk counts:-

k=1 c=6980.6133

k=2 c=24364481.

k=3 c=4275.4493

k=4 c=1.0003326

k=5 c=0.00026330492

Here is the output from the same program for your AP3 record:-

k=3 q=367453

M1=4077056.1 M2=8154112.1 c=1.0000511

digits: 159381.72

score=83.853401

PRP'ing: 163.82127 GHz-yrs (100.00000%)

APk-detection: 2.2318013 E-11 GHz-yrs (1.3623391 E-11%)

Total: 163.82127 GHz-yrs

APk counts:-

k=1 c=253.59636

k=2 c=32155.557

k=3 c=1.0000511

k=4 c=0.000041469329

I wonder how those PRP'ing estimates compare with your actual figures, and in particular, whether the AP3 record was about 10 times as burdensome? (It has a considerably higher "score".)

Mike - --- 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