[QUOTE=Mini-Geek;233680][URL]http://factordb.com/index.php?id=1100000000217066046[/URL]
2^2047+1919 is the first 2048 bit PRP.[/QUOTE]

363seconds.

Don't happen to have a 2667bit(-ish) PRP lying around?

Should take me 20minutes.

Running an old CPU...

Wasn't just laying around, (at least, somewhere I know of) but it was pretty easy to find (like this: [url]http://factordb.com/index.php?query=2^2666%2Bx&use=x&perpage=20&format=1&sent=1&PR=1&PRP=1&U=1&VP=1&EV=1&OD=1&VC=1&x=1001[/url]).
[url]http://factordb.com/index.php?id=1100000000217070172[/url]
2^2666+1029

[QUOTE=Mini-Geek;233683]Wasn't just laying around, (at least, somewhere I know of) but it was pretty easy to find (like this: [URL="http://factordb.com/index.php?query=2%5E2666%2Bx&use=x&perpage=20&format=1&sent=1&PR=1&PRP=1&U=1&VP=1&EV=1&OD=1&VC=1&x=1001"]http://factordb.com/index.php?query=2^2666%2Bx&use=x&perpage=20&format=1&sent=1&PR=1&PRP=1&U=1&VP=1&EV=1&OD=1&VC=1&x=1001[/URL]).
[URL]http://factordb.com/index.php?id=1100000000217070172[/URL]
2^2666+1029[/QUOTE]

Neat, hadn't quite gotten to that..

Guess I'll be back in ~20minutes.

Thanks. :smile:

Update:
[Comments]
2^2666+1029

[Running Times]
Initialization=0.54s
1stPhase=17mn 6s
2ndPhase=2mn 41s
Total=19mn 48s

Going for my own 3198b now, should take 43m10s...

[QUOTE=lorgix;233682]363seconds.

Don't happen to have a 2667bit(-ish) PRP lying around?

Should take me 20minutes.

Running an old CPU...[/QUOTE]

(p^3-1)/(31*(p-1)) is pretty close with
[code]
p=4559140439605246986775014500080619491137393968038218809386916913653757601446475026559811332421368359507920505895185254919739348053023229901825962204155006127588822724232154336220818951066228727207390838474033799684980687248357362065135673190000690224690381118921310664342695266014924491063412709702714515578144088314654458736594102004839199206420682333425574826721978559570557587638153114871881213126413[/code]

Ok, I'm running an old P4 3.0GHz. I've done some benchmarking with Primo 3.0.9.

Should anyone care;

The execution time can be described pretty well like this:

[time in seconds] = 10^(1.885ln([size of number, in bytes])-11.8)

('ln' being the natural logarithm)

examples:

952bit number ~15seconds = 0.25min 287dec
1657bit number ~151seconds = 2.5min 499dec
2667bit number ~1188seconds = 20min 803dec
4518bit number ~11610seconds = 3.2hrs 1360dec

According to my current data points a 1000digit number should take just under 51minutes.

[QUOTE=lorgix;233713]According to my current data points a 1000digit number should take just under 51minutes.[/QUOTE]

To check, (p^7-1)/(701*(p-1)) is 1003 digits with
[code]p=350873297696472849263554940124861908781733064121099920935059133235344055568237998266433669196875315422852864166507262278772631215309341496528243805213779596862544172993
[/code]

Primo is going to be slow with numbers of the form k * b^n +1 as well;

It performs an n+1 test; Not an n-1 test;

Try 895 * 2[sup]7526[/sup] + 1 (2269 digits)

I think I already found it via Proth, so I've verified it the moment I found it.

[QUOTE=3.14159;233730]Primo is going to be slow with numbers of the form k * b^n +1 as well;

It performs an n+1 test; Not an n-1 test;

Try 895 * 2[sup]7526[/sup] + 1 (2269 digits)[/QUOTE]
Actually, I thought Primo just does straight-up ECPP, which is going to be VERY slow for k*b^n+-1 numbers (which of course can be much more easily done with N-1/N+1). Unless Primo tries an N+1 (not N-1) test first just in case?

[QUOTE=mdettweiler;233732]Actually, I thought Primo just does straight-up ECPP, which is going to be VERY slow for k*b^n+-1 numbers (which of course can be much more easily done with N-1/N+1). Unless Primo tries an N+1 (not N-1) test first just in case?[/QUOTE]

It tries an N+1 once in a while;

Why is it slower for k * b^n ± 1 numbers anyway?

[QUOTE=3.14159;233733]It tries an N+1 once in a while;

Why is it slower for k * b^n ± 1 numbers anyway?[/QUOTE]

Seems to me Primo does that for every test it runs.

But I know to little about the math behind it..

(12^513+1)^2-2 is prime.