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Old 2021-07-01, 20:12   #23
SethTro
 
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I have internet setup now and I'm busy running ethernet cables all over. Thanks for everyone's patience and DMs checking if I was okay. The server should hopefully be up by Sunday morning.

Last fiddled with by SethTro on 2021-07-01 at 20:13
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Old 2021-07-07, 06:41   #24
robert44444uk
 
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Quote:
Originally Posted by SethTro View Post
I have internet setup now and I'm busy running ethernet cables all over. Thanks for everyone's patience and DMs checking if I was okay. The server should hopefully be up by Sunday morning.
The input page is now working https://primegaps.cloudygo.com/
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Old 2021-07-13, 02:31   #25
Bobby Jacobs
 
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Default Why I am underwhelmed by the last few maximal prime gaps

The last few maximal prime gaps seemed smaller than the expected maximal prime gap. Now, I know why. In another post, I conjectured that the maximum prime gap between primes up to p is approximately ln2(p)-(2*ln(p)*ln(ln(p))). I defined the Jacobs value of a gap to be (g-ln2(p)+(2*ln(p)*ln(ln(p))))/ln(p). Then, a Jacobs value of 0 would be an average maximal gap, a value of 1 would be a big maximal gap, and a value of -1 would be a small maximal gap. Here are the Jacobs values of the known maximal gaps.

2, 3, 1, -2.774068078741657E-4
3, 5, 2, 0.5850019473393445
7, 11, 4, 1.0194170587459925
23, 29, 6, 0.8427693920801025
89, 97, 8, 0.2151204218932354
113, 127, 14, 1.2014335975957555
523, 541, 18, 0.24572021013679826
887, 907, 20, -0.03652024352158025
1129, 1151, 22, -0.02150721463226403
1327, 1361, 34, 1.448387619815254
9551, 9587, 36, -0.8100577183892048
15683, 15727, 44, -0.5731101097730286
19609, 19661, 52, -0.044318784730949315
31397, 31469, 72, 1.270502655772665
155921, 156007, 86, 0.19713225629640171
360653, 360749, 96, -0.19530119032678306
370261, 370373, 112, 1.0149060902113427
492113, 492227, 114, 0.7373958069907232
1349533, 1349651, 118, -0.4611403308640233
1357201, 1357333, 132, 0.5220568928672134
2010733, 2010881, 148, 1.033147878685969
4652353, 4652507, 154, 0.14036146068116476
17051707, 17051887, 180, -0.21707747686074932
20831323, 20831533, 210, 1.258402597454145
47326693, 47326913, 220, 0.5200965832122922
122164747, 122164969, 222, -0.8502170210370023
189695659, 189695893, 234, -0.8892319752420521
191912783, 191913031, 248, -0.1730735352653388
387096133, 387096383, 250, -1.1626831960005015
436273009, 436273291, 282, 0.2623201147347242
1294268491, 1294268779, 288, -1.1673904115852733
1453168141, 1453168433, 292, -1.1579267965057205
2300942549, 2300942869, 320, -0.5705701565499374
3842610773, 3842611109, 336, -0.6563443731836452
4302407359, 4302407713, 354, -0.025270036477032205
10726904659, 10726905041, 382, -0.27705464505393207
20678048297, 20678048681, 384, -1.250147345715678
22367084959, 22367085353, 394, -0.9557070199950923
25056082087, 25056082543, 456, 1.4512178681058923
42652618343, 42652618807, 464, 0.8761319444431268
127976334671, 127976335139, 468, -0.7928312132556395
182226896239, 182226896713, 474, -1.1368024109318071
241160624143, 241160624629, 486, -1.133103779054893
297501075799, 297501076289, 490, -1.3230610013550814
303371455241, 303371455741, 500, -0.9765903793850329
304599508537, 304599509051, 514, -0.45375859265074997
416608695821, 416608696337, 516, -0.8961227372483432
461690510011, 461690510543, 532, -0.4692611765107444
614487453523, 614487454057, 534, -0.8689218000292784
738832927927, 738832928467, 540, -0.9527802901109655
1346294310749, 1346294311331, 582, -0.43007067428120926
1408695493609, 1408695494197, 588, -0.2914020442057517
1968188556461, 1968188557063, 602, -0.3558643155112367
2614941710599, 2614941711251, 652, 0.9173811138146628
7177162611713, 7177162612387, 674, -0.0574570952912501
13829048559701, 13829048560417, 716, 0.22504080783702007
19581334192423, 19581334193189, 766, 1.264869125563402
42842283925351, 42842283926129, 778, 0.2904504058143198
90874329411493, 90874329412297, 804, -0.18509610871942694
171231342420521, 171231342421327, 806, -1.202125940325487
218209405436543, 218209405437449, 906, 1.4183818893463445
1189459969825483, 1189459969826399, 916, -1.2297298698358887
1686994940955803, 1686994940956727, 924, -1.5939815003889521
1693182318746371, 1693182318747503, 1132, 4.331590450308519
43841547845541059, 43841547845542243, 1184, -0.1292269969948478
55350776431903243, 55350776431904441, 1198, -0.17389157190416654
80873624627234849, 80873624627236069, 1220, -0.27108837564182264
203986478517455989, 203986478517457213, 1224, -1.7763241380075703
218034721194214273, 218034721194215521, 1248, -1.2896653554305229
305405826521087869, 305405826521089141, 1272, -1.2753733168794827
352521223451364323, 352521223451365651, 1328, -0.13791061617203643
401429925999153707, 401429925999155063, 1356, 0.32401793693094755
418032645936712127, 418032645936713497, 1370, 0.5971215852470018
804212830686677669, 804212830686679111, 1442, 1.1853125062362995
1425172824437699411, 1425172824437700887, 1476, 0.9753154533071884
5733241593241196731, 5733241593241198219, 1488, -1.2112885884477058
6787988999657777797, 6787988999657779307, 1510, -0.9991650401801192
15570628755536096243, 15570628755536097769, 1526, -2.0836332971905804
17678654157568189057, 17678654157568190587, 1530, -2.213542051864597
18361375334787046697, 18361375334787048247, 1550, -1.8283253937088773

Notice that most of the maximal gaps have a Jacobs value between -2 and 2. A weird anomaly is the gap of 1132, which has a Jacobs value of 4.33. The gaps of 1526 and 1530 are the only maximal gaps with a Jacobs value below -2. The gap of 1550 is almost at -2. If this gap of 1552 is a maximal gap, then it will also have a low Jacobs value. That is why I believe we should have a lot bigger maximal prime gaps.
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Old 2021-07-15, 04:24   #26
CraigLo
 
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I got really lucky and found another.


1572 35.4308 18571673432051830099
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Old 2021-07-15, 10:33   #27
SethTro
 
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Amazing work Craig!


It's great to see the lower bound pushed upwards!
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Old 2021-07-15, 11:36   #28
ATH
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Gratz again!

Did you really test everything up to 264 + 1.249 * 1017 ?
This is 5.36 times further from 264 than your last gap.

What speed are you getting on the 1080 TI ? Either in time per interval, like time per 1012 or whatever, or interval per time, how far per hour or per day?
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Old 2021-07-15, 12:07   #29
rudy235
 
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This is so exciting. We now have a "probable maximum gap" with the highest merit of all gaps that have a good chance of being maximal. There are gaps with much higher merits but almost no chance of becoming maximal.

1572 35.4308 18571673432051830099

Previous Maximal Gaps in order of Merit.
  1. 1476 P19 = 1425172824437699411 35.3103
  2. 1552 PRP20 = 18470057946260698231 34.9844
  3. 1442 P18 = 804212830686677669 34.9757
  4. 1550 P20 = 18361375334787046697 34.9439
  5. 1510 P19 = 6787988999657777797 34.8234
  6. 1530 P20 = 17678654157568189057 34.5225
  7. 1526 P20 = 15570628755536096243 34.5312
So, should it become a maximal gap it will have the highest merit of all the maximals.

Congratulations.

Edit: The second gap in the list -1552- gap is not yet proven to be maximal.

Last fiddled with by rudy235 on 2021-07-15 at 12:22
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Old 2021-07-16, 04:25   #30
CraigLo
 
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Looking for gaps >= 1300 I search about 150E9/sec = 1.3E16/day. That's sieving with about 10k primes and doing 1 Fermat test.
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Old 2021-07-17, 11:14   #31
Bobby Jacobs
 
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Congratulations on finding another gap! It is amazing that there are so many maximal prime gaps so logarithmically close to the binary round number 264.
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Old 2021-07-19, 11:24   #32
robert44444uk
 
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Quote:
Originally Posted by CraigLo View Post
I got really lucky and found another.


1572 35.4308 18571673432051830099
Astonishing!
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Old 2021-07-27, 21:06   #33
rudy235
 
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Quote:
Originally Posted by CraigLo View Post
I got really lucky and found another.


1572 35.4308 18571673432051830099
i looked for it at the prime gap tables and it was not there. Did you report it?
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