New low weight project

Citrix · 2013-08-26, 21:11

Moderator's edit: Moved here from the Low weight stats page thread.
The related discussion about generating low weight coefficients is here.

Quote:

Originally Posted by Citrix

7393513980157211*2^193554-1 is prime!

Reserving
73369061163506189
72034954241261729
7393513980157211
12066462798697631
23009979551311559

Complete to n=1M, no new primes.
The other k's reserved above were already at 1M.
I am working on new low weight k's now, so I am unreserving the above.

lsoule · 2013-08-29, 14:20

I'll reserve the first two (73369061163506189 and 72034954241261729) for experimenting.

lsoule · 2013-09-05, 16:26

73369061163506189 and 72034954241261729 are now at n=3M with no new primes.

Citrix · 2013-10-09, 01:04

I have generated a new batch of low weight k's.
These are much smaller than the k's Thomas11 posted before and hence they can use the Zero-padded FFT and then takes 1/3 of the time to test.

I have generated a new weight formula that is more accurate than extended nash weight.

Feel free to reserve the k not listed below. It would be nice if we can get all of these to 2M.

Code:

k	new weight formula	extended nash weight		Tested upto
355262321784119	334	17	2	4.6M
706809843271963	348	51	2	400K
452565773039167	361	27	2	400K
596571372172469	373	23	2	400K
286565972092003	382	19	1	400K
265685529211859	387	32	1	400K
296990097378209	393	16	1	400K
586824605110333	406	29	2	400K
329604383181013	409	23	2	400K
449348815525481	413	19	2	400K
242081876749393	413	20	2	400K
151649765670817	430	41	2	400K
30402136144241	436	23	2	400K
569227451812807	437	20	2	400K
546088659477761	447	19	1	400K
174421373354771	447	20	2	400K
122586944321669	448	31	2	400K
427662785542799	450	39	2	400K
280418984909561	453	26	2	400K
9703351863493	453	32	2	400K
85877608135057	456	24	2	400K
571267621226129	458	50	2	400K
413338777986037	459	25	2	400K
508015032236651	466	21	2	400K
103432747403021	466	32	2	400K
606564403438897	468	19	1	400K
380289695293271	476	20	2	400K
294408177753337	477	22	2	400K
225184019593957	478	20	2	400K
633114842538613	479	34	2	400K
640520549022929	483	44	1	400K
456234152728799	484	23	2	400K
18047352362383	488	18	2	400K
290388549449203	488	22	2	400K
689369809338823	490	28	2	400K
578664594032099	492	19	2	400K
270003999160183	494	20	2	400K
70904559410129	494	38	2	400K
124855201083911	504	26	2	400K
129859680799207	505	23	2	400K
87131678294021	507	23	2	400K
309363900392467	508	94	1	400K
242539796323031	509	26	2	400K
481134684645673	513	19	2	400K
352406054088929	519	20	2	400K
583299325638817	519	26	2	400K
376161389883883	520	26	2	400K
612472684451819	520	30	2	400K
659819349704111	524	26	2	400K
151550479574083	533	27	1	400K

Thomas11 · 2013-10-09, 12:20

Thanks for sharing your candidates, Citrix!
Could you give some details about your "new weight formula"?

I'm taking the first ten candidates (apart from the one already tested to n=4.6M):

706809843271963 348 51 2 400K
452565773039167 361 27 2 400K
596571372172469 373 23 2 400K
286565972092003 382 19 1 400K
265685529211859 387 32 1 400K
296990097378209 393 16 1 400K
586824605110333 406 29 2 400K
329604383181013 409 23 2 400K
449348815525481 413 19 2 400K
242081876749393 413 20 2 400K

lsoule · 2013-10-09, 15:44

Earlier I said I was working on 73369061163506189. That was actually 7393513980157211. That k is complete up to n=5.8M. The other k, 72034954241261729, is complete up to and including n=5224788. I'm stopping work on both of these.

lsoule · 2013-10-09, 16:12

I'll take the next set of 10 from Citrix's list and run 400k-2M.

151649765670817 430 41 2 400K
30402136144241 436 23 2 400K
569227451812807 437 20 2 400K
546088659477761 447 19 1 400K
174421373354771 447 20 2 400K
122586944321669 448 31 2 400K
427662785542799 450 39 2 400K
280418984909561 453 26 2 400K
9703351863493 453 32 2 400K
85877608135057 456 24 2 400K

Citrix · 2013-10-09, 16:27

Just to clarify I am still working on the 50 candidates I posted... Thomas11 and lsoule-- the candidates you reserved are ones I am working on.

Please reserve from the txt file I posted there are 4000 more to choose from.

The 50 candidates I am working on are not sequential as the list in the file so please be careful when choosing k.

Citrix · 2013-10-09, 16:31

Sieve n=1 to 2,880,000 up to p=65536
For the remaining candidates check gcd for 2^2880-1 & remaining candidates.
Candidates with no factors is the weight.

lsoule · 2013-10-09, 16:42

Thanks! Now I see 'NOT listed below'

lsoule · 2013-10-09, 18:52

Let me try out these 5
144730753389727
112654045235503
336080953522813
486000558483997
381773338094339

2013-10-09, 16:27	#8
Citrix Jun 2003 3105₈ Posts	Just to clarify I am still working on the 50 candidates I posted... Thomas11 and lsoule-- the candidates you reserved are ones I am working on. Please reserve from the txt file I posted there are 4000 more to choose from. The 50 candidates I am working on are not sequential as the list in the file so please be careful when choosing k. Last fiddled with by Citrix on 2013-10-09 at 16:27

2013-10-09, 16:31	#9
Citrix Jun 2003 3×5×107 Posts	New weight formula Sieve n=1 to 2,880,000 up to p=65536 For the remaining candidates check gcd for 2^2880-1 & remaining candidates. Candidates with no factors is the weight.

2013-10-09, 18:52	#11
lsoule Nov 2004 California 11010101000₂ Posts	New low weight project Let me try out these 5 144730753389727 112654045235503 336080953522813 486000558483997 381773338094339

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2013-08-29, 14:20	#2
lsoule Nov 2004 California 3250₈ Posts	I'll reserve the first two (73369061163506189 and 72034954241261729) for experimenting.

2013-09-05, 16:26	#3
lsoule Nov 2004 California 11010101000₂ Posts	73369061163506189 and 72034954241261729 are now at n=3M with no new primes.

2013-10-09, 12:20	#5
Thomas11 Feb 2003 780₁₆ Posts	Thanks for sharing your candidates, Citrix! Could you give some details about your "new weight formula"? I'm taking the first ten candidates (apart from the one already tested to n=4.6M): 706809843271963 348 51 2 400K 452565773039167 361 27 2 400K 596571372172469 373 23 2 400K 286565972092003 382 19 1 400K 265685529211859 387 32 1 400K 296990097378209 393 16 1 400K 586824605110333 406 29 2 400K 329604383181013 409 23 2 400K 449348815525481 413 19 2 400K 242081876749393 413 20 2 400K

2013-10-09, 15:44	#6
lsoule Nov 2004 California 1704₁₀ Posts	Earlier I said I was working on 73369061163506189. That was actually 7393513980157211. That k is complete up to n=5.8M. The other k, 72034954241261729, is complete up to and including n=5224788. I'm stopping work on both of these.

2013-10-09, 16:12	#7
lsoule Nov 2004 California 11010101000₂ Posts	I'll take the next set of 10 from Citrix's list and run 400k-2M. 151649765670817 430 41 2 400K 30402136144241 436 23 2 400K 569227451812807 437 20 2 400K 546088659477761 447 19 1 400K 174421373354771 447 20 2 400K 122586944321669 448 31 2 400K 427662785542799 450 39 2 400K 280418984909561 453 26 2 400K 9703351863493 453 32 2 400K 85877608135057 456 24 2 400K

2013-10-09, 16:42	#10
lsoule Nov 2004 California 2³·3·71 Posts	Thanks! Now I see 'NOT listed below'