mersenneforum.org  

Go Back   mersenneforum.org > Prime Search Projects > Prime Gap Searches

Reply
 
Thread Tools
Old 2015-10-23, 06:11   #45
robert44444uk
 
robert44444uk's Avatar
 
Jun 2003
Oxford, UK

193310 Posts
Default

Quote:
Originally Posted by mart_r View Post
Before I jumped on the bandwagon with the (m*p#)/(d*q#)±x kind of sequences, I wrote a small code that tells me how many candidates there are left to check after a trial division up to p.
This gives sort of an "effective" merit, as displayed in this example:

Code:
center number = 2000003# / 13#
           numbers without
          factor <= 2000003  effective merit
           - side  + side    - side  + side
merit ± 1    2550    2527      0.03    0.03
merit ± 2    3218    3199      0.04    0.04
merit ± 3   21172   21119      0.27    0.27
merit ± 4   38603   38594      0.50    0.50
merit ± 5   64610   64486      0.84    0.83
merit ± 6   90082   90090      1.16    1.16
merit ± 7  127014  127067      1.64    1.64
merit ± 8  163654  163684      2.12    2.12
merit ± 9  204374  204397      2.64    2.64
merit ±10  244814  244884      3.17    3.17
Depending on the parameters, you can choose which merit you want to find, then take exp(effective merit) to have a rough estimate of the number of different tests you might need until an example is found.
If e.g. you aim for a merit >10 in this region (± 5), after four attempts there is a >50% chance that an example is found. (I loosely calculate this 50%-chance by using the factor log(2), so exp(0.84+0.83)*log(2) ~ 3.7 attempts)
Thanks mart_r. this is very instructive. I am being really thick though - how is "effective merit" calculated?

Last fiddled with by robert44444uk on 2015-10-23 at 06:12
robert44444uk is offline   Reply With Quote
Old 2015-10-23, 19:57   #46
mart_r
 
mart_r's Avatar
 
Dec 2008
you know...around...

2×52×13 Posts
Default

Quote:
Originally Posted by robert44444uk View Post
how is "effective merit" calculated?
Let W(p)=\prod_{p:prime} \frac {p-1}{p}

Then the number of numbers without a factor <=p must be divided by log(p#)*W(p) to get the "effective merit".

In my example then, one prime is expected every 77338th number without a factor <= 2000003 (log 2000003# * W(2000003) = 1998602.23 * 0.0386962947 = 77338.5009...).

On second thought, I should have explained this earlier... my bad.

By the way, does anyone know of a formula to get a sufficiently accurate value for W(p) without having to calculate it directly (e.g. if p is large), preferably using known values of Li(p)-\pi(p)?
I construed something which can be used with known values from Chebychev's theta:
W(p) ~ e^\gamma (\log p + \frac {2}{\sqrt p} - \frac {p-\theta (p)}{p})
I wonder if this can be improved somehow.


As you may notice, I'm also still actively searching for gaps from time to time, I only just gathered all data from the past twelve months and was overwhelmed that there were a total of 150 gaps for Mr Nicely's list! I was expecting maybe 50 or thereabouts...
mart_r is offline   Reply With Quote
Old 2015-10-31, 14:23   #47
robert44444uk
 
robert44444uk's Avatar
 
Jun 2003
Oxford, UK

111100011012 Posts
Default

Quote:
Originally Posted by mart_r View Post


As you may notice, I'm also still actively searching for gaps from time to time, I only just gathered all data from the past twelve months and was overwhelmed that there were a total of 150 gaps for Mr Nicely's list! I was expecting maybe 50 or thereabouts...
And what results - three of a million plus, the first additions to that list for a while. There were none in 2014

1176666 C?P MrtnRaab 2015 12.9561 39443 91199#/46473256830 - 547454
1217460 C?P MrtnRaab 2015 13.4036 39448 91229#/46093437390 - 495038
1462522 C?P MrtnRaab 2015 16.1016 39448 91229#/46056680670 - 853776
robert44444uk is offline   Reply With Quote
Old 2015-11-12, 16:11   #48
robert44444uk
 
robert44444uk's Avatar
 
Jun 2003
Oxford, UK

78D16 Posts
Default

Here are some statistics, banded by gap size, by discoverer and by year. 2008 was not a good year for surviving gaps! 2001 is the earliest year in which gaps >2k have survived, Pardo and Dubner seemed the only folks looking at larger gaps back then.

Danaj has over 90% of gaps in the 30-35K range but none >1,000K. Helmut Spielaur almost has 100% of the 2-4K range.

Here are the discoverers

Code:

Name	Total	0-2K	2-4K	4-6K	6-8K	8-10K	10-15K	15-20K	20-25K	25-30K	30-35K	35-40K	40-45K	45-50K	50-55K	55-60K	60-70K	70-80K	80-100K	100-150K	150-200K	200-1000K	>1000K
																							
Jacobsen	43502	0	3	24	262	639	1617	2009	2111	2201	2255	1901	1788	1917	1908	1696	3034	2768	5833	6637	2295	2604	0
Rosnthal	6111	0	4	3	17	37	215	77	38	9	13	49	80	33	42	58	283	526	717	3185	706	19	0
MJPC&JKA	5911	0	0	0	0	0	0	41	40	99	92	300	347	337	341	478	999	971	1148	220	48	448	2
M.Jansen	4638	0	0	2	17	36	193	227	182	164	114	213	196	130	110	123	212	88	108	569	669	1283	2
RobSmith	5308	0	0	0	2	8	37	20	25	15	5	2	3	7	7	14	100	279	1124	2266	899	495	0
Spielaur	2448	270	986	426	492	242	32	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
PierCami	1415	0	0	0	0	0	0	1	1	1	0	2	5	5	13	32	75	84	168	355	254	417	2
Gapcoin	1056	0	0	530	127	12	335	31	21	0	0	0	0	0	0	0	0	0	0	0	0	0	0
TorAlmJA	524	0	4	3	13	9	8	1	0	0	0	2	10	3	2	1	9	28	74	208	101	48	0
Toni_Key	3837	0	0	1	4	3	40	89	82	7	11	26	56	65	74	95	278	235	437	2019	307	8	0
Andersen	128	0	0	2	3	1	4	0	0	0	0	0	0	0	0	0	7	5	5	55	24	22	0
Be.Nyman	121	121	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
RP.Brent	120	120	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
TRNicely	95	95	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
LndrPrkn	72	72	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Yng&Ptlr	71	71	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
TOeSilva	70	70	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
HrzogTOS	52	52	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Glaisher	43	43	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
DHLehmer	38	38	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
JLGPardo	14	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	9	4	1	0
MrtnRaab	170	0	0	6	63	13	19	3	0	4	10	5	15	3	3	3	3	0	0	4	5	8	3
GABandAR	12	12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Other	64	36	3	3	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	2	1	14	4
																							
Total	75820	1000	1000	1000	1000	1000	2500	2500	2500	2500	2500	2500	2500	2500	2500	2500	5000	4984	9614	15529	5313	5367	13
Code:

Name	Total	0-2K	2-4K	4-6K	6-8K	8-10K	10-15K	15-20K	20-25K	25-30K	30-35K	35-40K	40-45K	45-50K	50-55K	55-60K	60-70K	70-80K	80-100K	100-150K	150-200K	200-1000K	>1000K
																							
Jacobsen	57.4%	0.0%	0.3%	2.4%	26.2%	63.9%	64.7%	80.4%	84.4%	88.0%	90.2%	76.0%	71.5%	76.7%	76.3%	67.8%	60.7%	55.5%	60.7%	42.7%	43.2%	48.5%	0.0%
Rosnthal	8.1%	0.0%	0.4%	0.3%	1.7%	3.7%	8.6%	3.1%	1.5%	0.4%	0.5%	2.0%	3.2%	1.3%	1.7%	2.3%	5.7%	10.6%	7.5%	20.5%	13.3%	0.4%	0.0%
MJPC&JKA	7.8%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	1.6%	1.6%	4.0%	3.7%	12.0%	13.9%	13.5%	13.6%	19.1%	20.0%	19.5%	11.9%	1.4%	0.9%	8.3%	15.4%
M.Jansen	6.1%	0.0%	0.0%	0.2%	1.7%	3.6%	7.7%	9.1%	7.3%	6.6%	4.6%	8.5%	7.8%	5.2%	4.4%	4.9%	4.2%	1.8%	1.1%	3.7%	12.6%	23.9%	15.4%
RobSmith	7.0%	0.0%	0.0%	0.0%	0.2%	0.8%	1.5%	0.8%	1.0%	0.6%	0.2%	0.1%	0.1%	0.3%	0.3%	0.6%	2.0%	5.6%	11.7%	14.6%	16.9%	9.2%	0.0%
Spielaur	3.2%	27.0%	98.6%	42.6%	49.2%	24.2%	1.3%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
PierCami	1.9%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	0.2%	0.2%	0.5%	1.3%	1.5%	1.7%	1.7%	2.3%	4.8%	7.8%	15.4%
Gapcoin	1.4%	0.0%	0.0%	53.0%	12.7%	1.2%	13.4%	1.2%	0.8%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
TorAlmJA	0.7%	0.0%	0.4%	0.3%	1.3%	0.9%	0.3%	0.0%	0.0%	0.0%	0.0%	0.1%	0.4%	0.1%	0.1%	0.0%	0.2%	0.6%	0.8%	1.3%	1.9%	0.9%	0.0%
Toni_Key	5.1%	0.0%	0.0%	0.1%	0.4%	0.3%	1.6%	3.6%	3.3%	0.3%	0.4%	1.0%	2.2%	2.6%	3.0%	3.8%	5.6%	4.7%	4.5%	13.0%	5.8%	0.1%	0.0%
Andersen	0.2%	0.0%	0.0%	0.2%	0.3%	0.1%	0.2%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	0.1%	0.1%	0.4%	0.5%	0.4%	0.0%
Be.Nyman	0.2%	12.1%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
RP.Brent	0.2%	12.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
TRNicely	0.1%	9.5%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
LndrPrkn	0.1%	7.2%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
Yng&Ptlr	0.1%	7.1%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
TOeSilva	0.1%	7.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
HrzogTOS	0.1%	5.2%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
Glaisher	0.1%	4.3%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
DHLehmer	0.1%	3.8%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
JLGPardo	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	0.1%	0.0%	0.0%
MrtnRaab	0.2%	0.0%	0.0%	0.6%	6.3%	1.3%	0.8%	0.1%	0.0%	0.2%	0.4%	0.2%	0.6%	0.1%	0.1%	0.1%	0.1%	0.0%	0.0%	0.0%	0.1%	0.1%	23.1%
GABandAR	0.0%	1.2%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
Other	0.1%	3.6%	0.3%	0.3%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.3%	30.8%
																							
Total	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%
robert44444uk is offline   Reply With Quote
Old 2015-11-12, 16:14   #49
robert44444uk
 
robert44444uk's Avatar
 
Jun 2003
Oxford, UK

1,933 Posts
Default

And here are the year breakdowns:

Code:
Year	Total	0-2K	2-4K	4-6K	6-8K	8-10K	10-15K	15-20K	20-25K	25-30K	30-35K	35-40K	40-45K	45-50K	50-55K	55-60K	60-70K	70-80K	80-100K	100-150K	150-200K	200-1000K	>1000K
																							
2015	44603	10	473	347	384	565	1277	1522	1324	999	1466	1090	775	993	1379	1498	3226	3203	6921	12014	2953	2181	3
2014	16419	59	236	351	166	223	975	687	927	1233	829	894	1170	1043	662	376	483	612	1183	2098	1259	953	0
2013	7097	49	100	177	275	114	37	67	99	138	99	302	348	336	352	487	1017	974	1180	253	71	619	3
2012	3934	66	103	78	143	69	138	196	125	72	63	136	89	45	59	83	148	65	41	400	603	1209	3
2011	1075	94	64	38	15	19	58	25	24	57	43	74	104	76	35	30	49	17	39	142	55	17	0
2010	704	52	15	3	0	0	0	2	0	0	0	0	0	0	0	4	37	55	98	293	87	57	1
2009	577	9	5	1	1	0	0	0	1	1	0	2	1	4	9	20	24	25	65	46	128	235	0
2008	18	14	0	0	0	0	3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
2007	340	17	3	0	5	3	2	0	0	0	0	1	5	2	1	2	8	19	45	129	63	35	0
2006	173	25	0	1	4	4	1	0	0	0	0	0	5	0	2	0	0	4	12	52	45	17	1
2005	18	16	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	0	0
2004	250	22	0	3	4	2	4	1	0	0	0	1	3	1	1	0	8	9	27	89	44	29	2
2003	44	15	1	1	3	1	5	0	0	0	0	0	0	0	0	0	0	1	3	1	0	13	0
2002	32	19	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	8	4	1	0
2001	26	23	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	3	0	0	0
2000	32	32	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
1999	36	36	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
1998	17	17	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
1997	16	16	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
1996	36	36	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
1995	12	12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
1994	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
1993	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Other	361	361	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
																							
Total	75820	1000	1000	1000	1000	1000	2500	2500	2500	2500	2500	2500	2500	2500	2500	2500	5000	4984	9614	15529	5313	5367	13
Code:
Year	Total	0-2K	2-4K	4-6K	6-8K	8-10K	10-15K	15-20K	20-25K	25-30K	30-35K	35-40K	40-45K	45-50K	50-55K	55-60K	60-70K	70-80K	80-100K	100-150K	150-200K	200-1000K	>1000K
																							
2015	58.8%	1.0%	47.3%	34.7%	38.4%	56.5%	51.1%	60.9%	53.0%	40.0%	58.6%	43.6%	31.0%	39.7%	55.2%	59.9%	64.5%	64.3%	72.0%	77.4%	55.6%	40.6%	23.1%
2014	21.7%	5.9%	23.6%	35.1%	16.6%	22.3%	39.0%	27.5%	37.1%	49.3%	33.2%	35.8%	46.8%	41.7%	26.5%	15.0%	9.7%	12.3%	12.3%	13.5%	23.7%	17.8%	0.0%
2013	9.4%	4.9%	10.0%	17.7%	27.5%	11.4%	1.5%	2.7%	4.0%	5.5%	4.0%	12.1%	13.9%	13.4%	14.1%	19.5%	20.3%	19.5%	12.3%	1.6%	1.3%	11.5%	23.1%
2012	5.2%	6.6%	10.3%	7.8%	14.3%	6.9%	5.5%	7.8%	5.0%	2.9%	2.5%	5.4%	3.6%	1.8%	2.4%	3.3%	3.0%	1.3%	0.4%	2.6%	11.3%	22.5%	23.1%
2011	1.4%	9.4%	6.4%	3.8%	1.5%	1.9%	2.3%	1.0%	1.0%	2.3%	1.7%	3.0%	4.2%	3.0%	1.4%	1.2%	1.0%	0.3%	0.4%	0.9%	1.0%	0.3%	0.0%
2010	0.9%	5.2%	1.5%	0.3%	0.0%	0.0%	0.0%	0.1%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.2%	0.7%	1.1%	1.0%	1.9%	1.6%	1.1%	7.7%
2009	0.8%	0.9%	0.5%	0.1%	0.1%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	0.0%	0.2%	0.4%	0.8%	0.5%	0.5%	0.7%	0.3%	2.4%	4.4%	0.0%
2008	0.0%	1.4%	0.0%	0.0%	0.0%	0.0%	0.1%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
2007	0.4%	1.7%	0.3%	0.0%	0.5%	0.3%	0.1%	0.0%	0.0%	0.0%	0.0%	0.0%	0.2%	0.1%	0.0%	0.1%	0.2%	0.4%	0.5%	0.8%	1.2%	0.7%	0.0%
2006	0.2%	2.5%	0.0%	0.1%	0.4%	0.4%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.2%	0.0%	0.1%	0.0%	0.0%	0.1%	0.1%	0.3%	0.8%	0.3%	7.7%
2005	0.0%	1.6%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
2004	0.3%	2.2%	0.0%	0.3%	0.4%	0.2%	0.2%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	0.0%	0.0%	0.0%	0.2%	0.2%	0.3%	0.6%	0.8%	0.5%	15.4%
2003	0.1%	1.5%	0.1%	0.1%	0.3%	0.1%	0.2%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.2%	0.0%
2002	0.0%	1.9%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	0.1%	0.0%	0.0%
2001	0.0%	2.3%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
2000	0.0%	3.2%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
1999	0.0%	3.6%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
1998	0.0%	1.7%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
1997	0.0%	1.6%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
1996	0.0%	3.6%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
1995	0.0%	1.2%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
1994	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
1993	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
Other	0.5%	36.1%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
																							
Total	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%
robert44444uk is offline   Reply With Quote
Old 2015-11-12, 17:12   #50
danaj
 
"Dana Jacobsen"
Feb 2011
Bangkok, TH

22·227 Posts
Default

Interesting tables, thanks for compiling and sharing! There has been a huge amount of activity this year compared to previous, from what I see.

The small gaps are interesting. I kind of want to see what an AWS instance churning on small numbers could do. It's not as exciting as the 60-100k range though, where every hour sees visible results. :)

For 1000k+, I stopped my largest search quite a while back, which is why my largest ones are now 300-400kish. Above 4k digits or so, a different library should be used -- gwnum is better than GMP for this. I was debating writing a script that would take as input something like '1 * 37993# / 30' and do the presieve with my code to get the list of candidates, then call OpenPFGW on each one to test compositeness until a PRP is found (which can then be tested with BPSW or Paul's gwnum-Frobenius routine). More polished would be a C program that pulls all that in.

I've debated running it anyway just to get some results, but it seems wrong to run code that I know is 2-10x slower than other methods. I keep hoping GMP will do something to narrow the distance. Version 6.1.0 just got released, with support for ADX on Broadwell and Skylake (none of my machines are that new) and "Tuned values for FFT multiplications are provided for larger number on many platforms" which could be helpful. I really need to try it out.
danaj is offline   Reply With Quote
Old 2015-11-13, 10:21   #51
robert44444uk
 
robert44444uk's Avatar
 
Jun 2003
Oxford, UK

1,933 Posts
Default

Quote:
Originally Posted by danaj View Post

For 1000k+, I stopped my largest search quite a while back, which is why my largest ones are now 300-400kish. Above 4k digits or so, a different library should be used -- gwnum is better than GMP for this. I was debating writing a script that would take as input something like '1 * 37993# / 30' and do the presieve with my code to get the list of candidates, then call OpenPFGW on each one to test compositeness until a PRP is found (which can then be tested with BPSW or Paul's gwnum-Frobenius routine). More polished would be a C program that pulls all that in.

I've debated running it anyway just to get some results, but it seems wrong to run code that I know is 2-10x slower than other methods. I keep hoping GMP will do something to narrow the distance. Version 6.1.0 just got released, with support for ADX on Broadwell and Skylake (none of my machines are that new) and "Tuned values for FFT multiplications are provided for larger number on many platforms" which could be helpful. I really need to try it out.
You should write this stuff!
robert44444uk is offline   Reply With Quote
Old 2015-11-13, 10:53   #52
robert44444uk
 
robert44444uk's Avatar
 
Jun 2003
Oxford, UK

193310 Posts
Default

And here are the last two summary stat tables:

Code:
merit	Total	0-2K	2-4K	4-6K	6-8K	8-10K	10-15K	15-20K	20-25K	25-30K	30-35K	35-40K	40-45K	45-50K	50-55K	55-60K	60-70K	70-80K	80-100K	100-150K	150-200K	200-1000K	>1000K
																							
35	2	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0
34	5	4	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
33	22	11	1	2	6	0	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0
32	43	17	0	3	15	0	0	0	1	1	1	0	0	1	1	0	1	1	0	1	0	0	0
31	100	36	6	3	38	0	2	3	1	3	2	2	2	1	0	0	1	0	0	0	0	0	0
30	178	38	24	54	14	2	7	3	5	5	9	2	3	1	1	3	2	1	2	1	1	0	0
29	367	55	60	114	10	11	20	19	17	11	13	6	8	3	4	3	2	5	5	1	0	0	0
28	688	63	156	151	27	14	29	46	45	38	25	22	18	11	8	6	10	10	5	2	1	1	0
27	1262	124	279	175	51	40	109	97	111	64	51	39	37	8	17	5	15	21	10	7	2	0	0
26	2005	138	336	186	108	100	212	204	177	135	90	109	55	36	18	8	37	23	15	11	3	4	0
25	2898	75	122	171	187	179	396	435	321	257	168	205	96	48	39	30	77	38	34	10	5	4	1
24	4303	30	15	113	303	285	622	632	507	411	375	315	123	109	61	69	143	72	67	40	6	5	0
23	5109	30	1	26	192	248	622	647	596	589	590	385	207	155	129	149	253	116	79	72	14	9	0
22	4902	34	0	2	47	104	382	323	488	523	658	376	368	217	257	287	357	202	138	106	18	15	0
21	4436	23	0	0	2	17	95	80	204	357	363	347	404	405	427	448	476	297	248	181	38	24	0
20	4365	26	0	0	0	0	3	9	26	97	120	343	399	508	598	415	675	381	410	267	50	38	0
19	4668	28	0	0	0	0	0	1	1	8	30	225	394	580	508	357	824	465	617	463	107	60	0
18	4406	26	0	0	0	0	0	0	0	0	5	91	296	302	242	348	675	655	788	717	193	68	0
17	4202	20	0	0	0	0	0	0	0	0	0	30	85	99	133	239	561	749	943	926	312	105	0
16	4189	24	0	0	0	0	0	0	0	0	0	3	5	14	48	84	408	611	1158	1259	429	145	1
15	4282	17	0	0	0	0	0	0	0	0	0	0	0	2	9	37	290	498	1162	1451	556	258	2
14	4182	23	0	0	0	0	0	0	0	0	0	0	0	0	0	9	102	334	1292	1861	215	345	1
13	4245	20	0	0	0	0	0	0	0	0	0	0	0	0	0	2	52	226	913	2300	247	484	1
12	3782	19	0	0	0	0	0	0	0	0	0	0	0	0	0	1	20	158	513	2120	323	625	3
11	3295	15	0	0	0	0	0	0	0	0	0	0	0	0	0	0	12	73	377	1642	470	704	2
10	2513	16	0	0	0	0	0	0	0	0	0	0	0	0	0	0	4	16	306	893	602	675	1
9	1637	15	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	9	370	252	362	628	0
8	1327	14	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	10	111	240	416	536	0
7	951	11	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	5	11	195	409	318	1
6	734	10	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	4	8	198	324	190	0
5	411	10	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	12	173	103	112	0
4	215	8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	11	99	81	14	0
3	75	8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	8	32	26	0	0
2	17	7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	9	0	0	0
1	4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
																							
Total	75820	1000	1000	1000	1000	1000	2500	2500	2500	2500	2500	2500	2500	2500	2500	2500	5000	4984	9614	15529	5313	5367	13
Code:
merit	Total	0-2K	2-4K	4-6K	6-8K	8-10K	10-15K	15-20K	20-25K	25-30K	30-35K	35-40K	40-45K	45-50K	50-55K	55-60K	60-70K	70-80K	80-100K	100-150K	150-200K	200-1000K	>1000K
																							
35	0.0%	0.1%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
34	0.0%	0.4%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
33	0.0%	1.1%	0.1%	0.2%	0.6%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
32	0.1%	1.7%	0.0%	0.3%	1.5%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
31	0.1%	3.6%	0.6%	0.3%	3.8%	0.0%	0.1%	0.1%	0.0%	0.1%	0.1%	0.1%	0.1%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
30	0.2%	3.8%	2.4%	5.4%	1.4%	0.2%	0.3%	0.1%	0.2%	0.2%	0.4%	0.1%	0.1%	0.0%	0.0%	0.1%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
29	0.5%	5.5%	6.0%	11.4%	1.0%	1.1%	0.8%	0.8%	0.7%	0.4%	0.5%	0.2%	0.3%	0.1%	0.2%	0.1%	0.0%	0.1%	0.1%	0.0%	0.0%	0.0%	0.0%
28	0.9%	6.3%	15.6%	15.1%	2.7%	1.4%	1.2%	1.8%	1.8%	1.5%	1.0%	0.9%	0.7%	0.4%	0.3%	0.2%	0.2%	0.2%	0.1%	0.0%	0.0%	0.0%	0.0%
27	1.7%	12.4%	27.9%	17.5%	5.1%	4.0%	4.4%	3.9%	4.4%	2.6%	2.0%	1.6%	1.5%	0.3%	0.7%	0.2%	0.3%	0.4%	0.1%	0.0%	0.0%	0.0%	0.0%
26	2.6%	13.8%	33.6%	18.6%	10.8%	10.0%	8.5%	8.2%	7.1%	5.4%	3.6%	4.4%	2.2%	1.4%	0.7%	0.3%	0.7%	0.5%	0.2%	0.1%	0.1%	0.1%	0.0%
25	3.8%	7.5%	12.2%	17.1%	18.7%	17.9%	15.8%	17.4%	12.8%	10.3%	6.7%	8.2%	3.8%	1.9%	1.6%	1.2%	1.5%	0.8%	0.4%	0.1%	0.1%	0.1%	7.7%
24	5.7%	3.0%	1.5%	11.3%	30.3%	28.5%	24.9%	25.3%	20.3%	16.4%	15.0%	12.6%	4.9%	4.4%	2.4%	2.8%	2.9%	1.4%	0.7%	0.3%	0.1%	0.1%	0.0%
23	6.7%	3.0%	0.1%	2.6%	19.2%	24.8%	24.9%	25.9%	23.8%	23.6%	23.6%	15.4%	8.3%	6.2%	5.2%	6.0%	5.1%	2.3%	0.8%	0.5%	0.3%	0.2%	0.0%
22	6.5%	3.4%	0.0%	0.2%	4.7%	10.4%	15.3%	12.9%	19.5%	20.9%	26.3%	15.0%	14.7%	8.7%	10.3%	11.5%	7.1%	4.1%	1.4%	0.7%	0.3%	0.3%	0.0%
21	5.9%	2.3%	0.0%	0.0%	0.2%	1.7%	3.8%	3.2%	8.2%	14.3%	14.5%	13.9%	16.2%	16.2%	17.1%	17.9%	9.5%	6.0%	2.6%	1.2%	0.7%	0.4%	0.0%
20	5.8%	2.6%	0.0%	0.0%	0.0%	0.0%	0.1%	0.4%	1.0%	3.9%	4.8%	13.7%	16.0%	20.3%	23.9%	16.6%	13.5%	7.6%	4.3%	1.7%	0.9%	0.7%	0.0%
19	6.2%	2.8%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.3%	1.2%	9.0%	15.8%	23.2%	20.3%	14.3%	16.5%	9.3%	6.4%	3.0%	2.0%	1.1%	0.0%
18	5.8%	2.6%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.2%	3.6%	11.8%	12.1%	9.7%	13.9%	13.5%	13.1%	8.2%	4.6%	3.6%	1.3%	0.0%
17	5.5%	2.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	1.2%	3.4%	4.0%	5.3%	9.6%	11.2%	15.0%	9.8%	6.0%	5.9%	2.0%	0.0%
16	5.5%	2.4%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	0.2%	0.6%	1.9%	3.4%	8.2%	12.3%	12.0%	8.1%	8.1%	2.7%	7.7%
15	5.6%	1.7%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	0.4%	1.5%	5.8%	10.0%	12.1%	9.3%	10.5%	4.8%	15.4%
14	5.5%	2.3%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.4%	2.0%	6.7%	13.4%	12.0%	4.0%	6.4%	7.7%
13	5.6%	2.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	1.0%	4.5%	9.5%	14.8%	4.6%	9.0%	7.7%
12	5.0%	1.9%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.4%	3.2%	5.3%	13.7%	6.1%	11.6%	23.1%
11	4.3%	1.5%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.2%	1.5%	3.9%	10.6%	8.8%	13.1%	15.4%
10	3.3%	1.6%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	0.3%	3.2%	5.8%	11.3%	12.6%	7.7%
9	2.2%	1.5%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.2%	3.8%	1.6%	6.8%	11.7%	0.0%
8	1.8%	1.4%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.2%	1.2%	1.5%	7.8%	10.0%	0.0%
7	1.3%	1.1%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	0.1%	1.3%	7.7%	5.9%	7.7%
6	1.0%	1.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	0.1%	1.3%	6.1%	3.5%	0.0%
5	0.5%	1.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	1.1%	1.9%	2.1%	0.0%
4	0.3%	0.8%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	0.6%	1.5%	0.3%	0.0%
3	0.1%	0.8%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	0.2%	0.5%	0.0%	0.0%
2	0.0%	0.7%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.1%	0.0%	0.0%	0.0%
1	0.0%	0.4%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
robert44444uk is offline   Reply With Quote
Old 2015-11-17, 16:22   #53
danaj
 
"Dana Jacobsen"
Feb 2011
Bangkok, TH

22×227 Posts
Default

The range would be 20 to 8700 digits (realistically 700 to 8700) -- I meant that we want every entry to have a merit at least 5. 6 would do, but so would 10, 15, 20, 25, 30, and we'd welcome 35 with joyous hearts.

Last fiddled with by danaj on 2015-11-17 at 16:25
danaj is offline   Reply With Quote
Old 2015-12-03, 18:03   #54
danaj
 
"Dana Jacobsen"
Feb 2011
Bangkok, TH

22×227 Posts
Default

Quote:
Originally Posted by Antonio View Post
As it has been so long since the merits file has been updated, I've started to keep a local copy updated with my own results to prevent me from submitting spurious data.
Don't you have to do this anyway to prevent duplicates (two records for the same gap)? It is quite common for me to see duplicates during a week, and the 235 run I'm doing now will sometimes spit out two dups within minutes (out of 165 records output, there are 141 unique gap lengths).

This is one reason I put off submitting every week. It's not unusual for the next week to find quite a few better results, so putting it off means fewer intermediates. But I have been dropping down to every 2-3 weeks. I figure when I have 2k-3k new records I should get them pushed.

I submitted 2857 gaps on Nov 21. Min 3388, Max 522892, max merit 30.481935.

My current set is 1764 gaps. Min 4162, Max 521074, max merit 31.846851.

I have some searches going on in the sub 10k range, which makes for nice merits, but it is definitely slower in gaps/day than the 70k+ range.
danaj is offline   Reply With Quote
Old 2015-12-03, 20:22   #55
Antonio
 
Antonio's Avatar
 
"Antonio Key"
Sep 2011
UK

21316 Posts
Default

Quote:
Originally Posted by danaj View Post
Don't you have to do this anyway to prevent duplicates (two records for the same gap)? It is quite common for me to see duplicates during a week, and the 235 run I'm doing now will sometimes spit out two dups within minutes (out of 165 records output, there are 141 unique gap lengths).

This is one reason I put off submitting every week. It's not unusual for the next week to find quite a few better results, so putting it off means fewer intermediates. But I have been dropping down to every 2-3 weeks. I figure when I have 2k-3k new records I should get them pushed.

I submitted 2857 gaps on Nov 21. Min 3388, Max 522892, max merit 30.481935.

My current set is 1764 gaps. Min 4162, Max 521074, max merit 31.846851.

I have some searches going on in the sub 10k range, which makes for nice merits, but it is definitely slower in gaps/day than the 70k+ range.
While the merits file was being updated once or more a week, I was checking my weeks work for duplicates and then against the latest merits file just before submitting. I was not, however, checking against my earlier submissions as they were already in the latest merits file.
I have also modified the search script so that it re-reads the merits.txt file every 12 hrs. (at a convenient point in the program, so this is only approximate) to reduce any redundant output, if/when the merit file is updated. This may change to once every 24 hrs., but it only takes a second or two, and is much more convenient than stopping and re-starting the script.
I backup the results files from all four threads each morning and this now automatically also updates my local merits.txt, so now each thread 'knows' about the other threads results within 12 hrs. of the backup.

I was submitting about 500-600 results each week, but since starting the search for the missing gaps < 100k this has dropped and is now at about 350 per week.
Antonio is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
News gd_barnes Conjectures 'R Us 299 2021-02-19 09:30
News gd_barnes No Prime Left Behind 251 2021-02-15 03:00
P!=NP in the news willmore Computer Science & Computational Number Theory 48 2010-09-19 08:30
The news giveth, the news taketh away... NBtarheel_33 Hardware 17 2009-05-04 15:52
Some news about Home Prime ? MoZ Factoring 6 2006-02-28 12:02

All times are UTC. The time now is 08:15.

Wed May 12 08:15:27 UTC 2021 up 34 days, 2:56, 0 users, load averages: 1.95, 1.82, 1.87

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.