New low weight project - Page 2

Thomas11 · 2013-10-09, 20:46

Well, then I'm taking the next ten from the list:

400588116807757
51767003109907
515228162892643
370808104333991
252739684100143
288026236187293
554018578982563
199128666830563
105384434582653
288679463759563

Citrix · 2013-10-09, 22:31

I have updated the list

Code:

k	new weight formula	At	Who 	Primes
355262321784119	334	4.6M	Citrix	
706809843271963	348	400K	Citrix	
452565773039167	361	400K	Citrix	
596571372172469	373	400K	Citrix	
286565972092003	382	400K	Citrix	
265685529211859	387	400K	Citrix	
296990097378209	393	400K	Citrix	
586824605110333	406	400K	Citrix	
329604383181013	409	400K	Citrix	
449348815525481	413	400K	Citrix	
242081876749393	413	400K	Citrix	
151649765670817	430	400K	Citrix	
30402136144241	436	400K	Citrix	
569227451812807	437	400K	Citrix	
546088659477761	447	400K	Citrix	
174421373354771	447	400K	Citrix
122586944321669	448	400K	Citrix
427662785542799	450	400K	Citrix
280418984909561	453	400K	Citrix
9703351863493	453	400K	Citrix
85877608135057	456	400K	Citrix
571267621226129	458	400K	Citrix
413338777986037	459	400K	Citrix
508015032236651	466	400K	Citrix
103432747403021	466	400K	Citrix
606564403438897	468	400K	Citrix
380289695293271	476	400K	Citrix
294408177753337	477	400K	Citrix
225184019593957	478	400K	Citrix
633114842538613	479	400K	Citrix
640520549022929	483	400K	Citrix    328
456234152728799	484	400K	Citrix
18047352362383	488	400K	Citrix
290388549449203	488	400K	Citrix
689369809338823	490	400K	Citrix
578664594032099	492	400K	Citrix
270003999160183	494	400K	Citrix
70904559410129	494	400K	Citrix
124855201083911	504	400K	Citrix
129859680799207	505	400K	Citrix
87131678294021	507	400K	Citrix
309363900392467	508	400K	Citrix
242539796323031	509	400K	Citrix
481134684645673	513	400K	Citrix
352406054088929	519	400K	Citrix
583299325638817	519	400K	Citrix
376161389883883	520	400K	Citrix
612472684451819	520	400K	Citrix
659819349704111	524	400K	Citrix
30190942754953	525		
723349170914983	528		
452386511160487	530		
327215225289341	530		
396620182602029	532		
151550479574083	533	400K	Citrix
144730753389727	536	5M	lsoule
112654045235503	541	2M	lsoule
336080953522813	541	2M	lsoule
486000558483997	542	2M	lsoule
381773338094339	542	2M	lsoule    10560
133594474062667	544	1.8M	Thomas11
400588116807757	545	2M	Thomas11
51767003109907	547	2M	Thomas11
515228162892643	547	2M	Thomas11
370808104333991	549	2M	Thomas11
252739684100143	549	2M	Thomas11
288026236187293	552	2M	Thomas11
554018578982563	554	2M	Thomas11
199128666830563	555	2M	Thomas11
105384434582653	557	2M	Thomas11
288679463759563	557	2M	Thomas11
350889331826233	559	1M	Thomas11
      ...	...	1M	Thomas11
626217613073557	625	1M	Thomas11
652851979787233	626	1.2M	lsoule
      ...	...	1.2M	lsoule
213642298225841	670	1.2M	lsoule

This list only lists the first few 100 k's.
Please update the list if you are reserving more k.

Citrix · 2013-10-11, 02:34

Thomas11 and lsoule,
How are you sieving for these k? Is srsieve better for multiple k or sieve each k using sr1sieve? How deep are you sieving?

I am finding some benefit with ECM and P-1 since srsieve is not able to sieve very deep.

What has your experience been like?

Thomas11 · 2013-10-11, 11:34

Quote:

Originally Posted by Citrix

Thomas11 and lsoule,
How are you sieving for these k?

I'm using srsieve. For less than about 10 k individual sieving using sr1sieve might be faster. For extremely low weights it can be useful to play with some of the parameters of sr1sieve, e.g. the options -B, -G, and -Q (forcing baby step and giant step or some specific subsequences), and whether precomputed tables for the Legendre symbols are used or not.
I remember that in one case I did some changes to the source code to get rid of some limitation there (e.g. to allow subsequences larger than 2^5760). But I don't have this at hand right now...

There is also Phil Carmody's ksieve which is the only choice if k>2^62. But for the smaller k I found srsieve to be faster.

ECM and/or P-1 testing might be an option for n>2M. I used this years ago during the 3*2^n-1 project.
Citrix, which software have you used for your tests, prime95, gmp-ecm, or something else?

lsoule · 2013-10-11, 14:36

I'm also using srsieve and took the 5 sequences up to p=350Bn (I forget but it was on the order of a day). The time between primes at that point was about the time it takes llr to test a candidate around n=1.6M on the same machine.

I haven't looked into optimizing the flow yet though. It would be nice if srsieve had the mutli-threaded option like sr1sieve for convenience though it could be split across cores manually.

Citrix · 2013-10-11, 17:47

I am using Prime95 for p-1/ECM. Using p-1 I can find about 2 factors/hour.

For 50 k's on srsieve I am getting 750k/sec (for nmax=5M)
Using Sr1sieve I am getting around 40M/sec for 1 k. (for nmax=5M)
(almost the same speed).
After sieving to 200G I have about 10000 candidates from n=1 M to 5 M for 50 K's. On average 50 candidates per k per million.

-Q option seems interesting
All the candidates that I generated have 1-2 numbers left (mod 2^2880-1)
ie the covering length is 2880.

Srsieve does not allow -Q option
Sr1sieve does... but is limited to 720.
One way of overcoming this is changing everything to base 256 or 4096 (any 2^n up to 2^14).
I am not sure if this will be faster or not, but will create a lot of overhead work.

Citrix · 2013-10-11, 21:38

converting to base 16, 256 or 4096 increases the speed of srsieve by 25%.
I did not use -Q. It may be useful with sr1sieve.

Thomas11 · 2013-10-12, 15:28

My 10 Ks are now fully tested for n=0-1.5M, and I will continue them to n=2M.

To get some more experience on optimal sieving, I'm also taking the next 100 Ks, from k=350889331826233 to k=626217613073557.

Thomas11 · 2013-10-12, 18:12

And I already got a few small primes from the bunch of 100 Ks.

The (k,n) pairs are:
350889331826233 311
6919997606293 331
390616763840893 355
72057272131093 447
512416936093019 65436

The current testing limit is n=75k.

lsoule · 2013-10-15, 15:28

144730753389727 is at n=5M
112654045235503, 336080953522813, 486000558483997, 381773338094339 are at n=2M.

One small prime so far 381773338094339*2^10560-1.

pinhodecarlos · 2013-10-15, 15:47

Quote:

Originally Posted by lsoule

144730753389727 is at n=5M

A question, how many candidates did you test until you reached 5M? Thank you in advance.

Carlos

2013-10-11, 17:47	#17
Citrix Jun 2003 3053₈ Posts	I am using Prime95 for p-1/ECM. Using p-1 I can find about 2 factors/hour. For 50 k's on srsieve I am getting 750k/sec (for nmax=5M) Using Sr1sieve I am getting around 40M/sec for 1 k. (for nmax=5M) (almost the same speed). After sieving to 200G I have about 10000 candidates from n=1 M to 5 M for 50 K's. On average 50 candidates per k per million. -Q option seems interesting All the candidates that I generated have 1-2 numbers left (mod 2^2880-1) ie the covering length is 2880. Srsieve does not allow -Q option Sr1sieve does... but is limited to 720. One way of overcoming this is changing everything to base 256 or 4096 (any 2^n up to 2^14). I am not sure if this will be faster or not, but will create a lot of overhead work. Last fiddled with by Citrix on 2013-10-11 at 17:54

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2013-10-09, 20:46	#12
Thomas11 Feb 2003 774₁₆ Posts	Well, then I'm taking the next ten from the list: 400588116807757 51767003109907 515228162892643 370808104333991 252739684100143 288026236187293 554018578982563 199128666830563 105384434582653 288679463759563

2013-10-11, 02:34	#14
Citrix Jun 2003 1,579 Posts	Thomas11 and lsoule, How are you sieving for these k? Is srsieve better for multiple k or sieve each k using sr1sieve? How deep are you sieving? I am finding some benefit with ECM and P-1 since srsieve is not able to sieve very deep. What has your experience been like?

2013-10-11, 14:36	#16
lsoule Nov 2004 California 11010101000₂ Posts	I'm also using srsieve and took the 5 sequences up to p=350Bn (I forget but it was on the order of a day). The time between primes at that point was about the time it takes llr to test a candidate around n=1.6M on the same machine. I haven't looked into optimizing the flow yet though. It would be nice if srsieve had the mutli-threaded option like sr1sieve for convenience though it could be split across cores manually.

2013-10-11, 21:38	#18
Citrix Jun 2003 1,579 Posts	converting to base 16, 256 or 4096 increases the speed of srsieve by 25%. I did not use -Q. It may be useful with sr1sieve.

2013-10-12, 15:28	#19
Thomas11 Feb 2003 2²×3²×53 Posts	My 10 Ks are now fully tested for n=0-1.5M, and I will continue them to n=2M. To get some more experience on optimal sieving, I'm also taking the next 100 Ks, from k=350889331826233 to k=626217613073557.

2013-10-12, 18:12	#20
Thomas11 Feb 2003 2²·3²·53 Posts	And I already got a few small primes from the bunch of 100 Ks. The (k,n) pairs are: 350889331826233 311 6919997606293 331 390616763840893 355 72057272131093 447 512416936093019 65436 The current testing limit is n=75k.

2013-10-15, 15:28	#21
lsoule Nov 2004 California 2³·3·71 Posts	144730753389727 is at n=5M 112654045235503, 336080953522813, 486000558483997, 381773338094339 are at n=2M. One small prime so far 381773338094339*2^10560-1.