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2015-10-23, 06:11   #45
robert44444uk

Jun 2003
Oxford, UK

191810 Posts

Quote:
 Originally Posted by mart_r 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

2015-10-23, 19:57   #46
mart_r

Dec 2008
you know...around...

22×5×31 Posts

Quote:
 Originally Posted by robert44444uk 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...

2015-10-31, 14:23   #47
robert44444uk

Jun 2003
Oxford, UK

2×7×137 Posts

Quote:
 Originally Posted by mart_r 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

 2015-11-12, 16:11 #48 robert44444uk     Jun 2003 Oxford, UK 2·7·137 Posts 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%
 2015-11-12, 16:14 #49 robert44444uk     Jun 2003 Oxford, UK 2·7·137 Posts 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%
 2015-11-12, 17:12 #50 danaj   "Dana Jacobsen" Feb 2011 Bangkok, TH 2·3·151 Posts 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.
2015-11-13, 10:21   #51
robert44444uk

Jun 2003
Oxford, UK

35768 Posts

Quote:
 Originally Posted by danaj 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!

 2015-11-13, 10:53 #52 robert44444uk     Jun 2003 Oxford, UK 2×7×137 Posts 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%
 2015-11-17, 16:22 #53 danaj   "Dana Jacobsen" Feb 2011 Bangkok, TH 2·3·151 Posts 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
2015-12-03, 18:03   #54
danaj

"Dana Jacobsen"
Feb 2011
Bangkok, TH

2×3×151 Posts

Quote:
 Originally Posted by Antonio 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.

2015-12-03, 20:22   #55
Antonio

"Antonio Key"
Sep 2011
UK

21316 Posts

Quote:
 Originally Posted by danaj 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.

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