Due to the recent finds I updated the Sierpinski record table (no changes after 150/75000):

[CODE]
S 1 10 1/1
S 1 10 2/2
S 1 10 3/3
S 3375 10 4/4
S 10753 10 5/5
S 46453 10 6/6
S 46453 10 7/7
S 935595 12 8/8
S 513427745633 58 9/9
S 2605422806599 52 10/10
S 5769236411869 52 11/11
S 315189 12 12/13
S 32133627572531 52 13/14
S 30738862614223 52 14/16
S 37033967202305 58 15/19
S 21583913743827 52 16/22
S 56385874414455 58 17/25
S 6748973546095 52 18/28
S 6748973546095 52 19/29
S 64827158861237 58 20/32
S 64827158861237 58 21/33
S 64827158861237 58 22/35
S 64827158861237 58 23/38
S 25000425620685 52 24/49
S 25000425620685 52 25/50
S 25000425620685 52 26/57
S 68247229126023 58 27/64
S 36877088213143 58 28/72
S 5277998474135 52 29/78
S 3527441029583 52 30/80
S 36877088213143 58 31/84
S 36877088213143 58 32/85
S 29312484587 52 33/96
S 15335838265589 52 34/99
S 15335838265589 52 35/102
S 15335838265589 52 36/109
S 3527441029583 52 37/120
S 15335838265589 52 38/133
S 71681789688525 52 39/142
S 36877088213143 58 40/154
S 36877088213143 58 41/158
S 391170716069 60 42/173
S 3527441029583 52 43/174
S 3527441029583 52 44/180
S 3527441029583 52 45/186
S 3527441029583 52 46/194
S 3527441029583 52 47/196
S 9525566335345 52 48/261
S 38988807163555 52 49/268
S 38988807163555 52 50/270
S 38988807163555 52 51/272
S 38988807163555 52 52/302
S 38988807163555 52 53/304
S 38988807163555 52 54/308
S 38988807163555 52 55/327
S 38988807163555 52 56/331
S 29732764305757 52 57/410
S 29732764305757 52 58/417
S 9918767791013 52 59/428
S 29732764305757 52 60/479
S 29732764305757 52 61/533
S 35578296845517 58 62/551
S 29732764305757 52 63/569
S 792030929331 58 64/589
S 792030929331 58 65/605
S 792030929331 58 66/612
S 792030929331 58 67/682
S 792030929331 58 68/735
S 35578296845517 58 69/769
S 35578296845517 58 70/810
S 71396794252893 52 71/916
S 47143850962579 52 72/936
S 71396794252893 52 73/951
S 71396794252893 52 74/1034
S 71396794252893 52 75/1145
S 13223354076641 52 76/1208
S 13223354076641 52 77/1229
S 1244513437798920 100 78/1332
S 2442649832339 58 79/1421
S 10068624641847 66 80/1487
S 5629710597113 52 81/1565
S 5629710597113 52 82/1638
S 5629710597113 52 83/1678
S 5629710597113 52 84/1691
S 5629710597113 52 85/1769
S 1108828374241 52 86/1861
S 1108828374241 52 87/1880
S 1108828374241 52 88/1892
S 1108828374241 52 89/1946
S 1108828374241 52 90/1951
S 1108828374241 52 91/1971
S 1108828374241 52 92/2044
S 1108828374241 52 93/2130
S 1108828374241 52 94/2150
S 1108828374241 52 95/2227
S 1108828374241 52 96/2328
S 1108828374241 52 97/2393
S 73647651306083 52 98/3028
S 73647651306083 52 99/3081
S 73647651306083 52 100/3167
S 1108828374241 52 101/3289
S 1108828374241 52 102/3405
S 1108828374241 52 103/3436
S 1108828374241 52 104/3450
S 1108828374241 52 105/3722
S 1108828374241 52 106/3833
S 1108828374241 52 107/4172
S 1108828374241 52 108/4227
S 1108828374241 52 109/4337
S 1108828374241 52 110/4495
S 73647651306083 52 111/7362
S 73647651306083 52 112/7365
S 31012884643679 52 113/8571
S 73647651306083 52 114/8817
S 73647651306083 52 115/8833
S 73647651306083 52 116/9159
S 73647651306083 52 117/9294
S 73647651306083 52 118/9463
S 73647651306083 52 119/9626
S 73647651306083 52 120/11090
S 12507984303339 60 121/12197
S 31012884643679 52 122/13391
S 2158430601663 66 123/15264
S 2158430601663 66 124/15317
S 2158430601663 66 125/15870
S 2158430601663 66 126/16937
S 12034494960083 66 127/18320
S 12034494960083 66 128/18523
S 2158430601663 66 129/19436
S 2158430601663 66 130/19593
S 2158430601663 66 131/22000
S 12034494960083 66 132/23001
S 732478130807511 106 133/25264
S 26465530345417 66 134/25891
S 732478130807511 106 135/26926
S 2001098777223151 100 136/32848
S 2001098777223151 100 137/33498
S 1437260117884190 106 138/35206
S 26465530345417 66 139/37658
S 26465530345417 66 140/38870
S 26465530345417 66 141/41219
S 26465530345417 66 142/41687
S 26465530345417 66 143/49380
S 26465530345417 66 144/49642
S 3488826124671 58 145/53941
S 26465530345417 66 146/56958
S 732478130807511 106 147/59441
S 16196964114523 58 148/63389
S 732478130807511 106 149/71777
S 16196964114523 58 150/74661
[/CODE]

For the sake of completeness (e.g. the missing data for [B]R 638621868573 60[/B] and the question marks in the Riesel record table) I repeated the calculations of Carmody and Chaglassian on this sequence up to n=101K.
I will continue this until the remaining 4 PRPs are rediscovered (n<165K) but at a much lower priority.

Here are the missing PRPs (for complete list see attached file):
638621868573*3*5*11*13*19*29*37*53*59*61*2^39070-1 (PRP 135)
638621868573*3*5*11*13*19*29*37*53*59*61*2^40467-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^41936-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^44644-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^45080-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^47148-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^49504-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^50232-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^55929-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^58502-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^61220-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^65223-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^69969-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^70169-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^73685-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^77167-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^80961-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^84012-1
638621868573*3*5*11*13*19*29*37*53*59*61*2^100101-1 (PRP 153)

So the record table should read as follows (no question marks any more):

[CODE]
R 24214294944371 82 137/36424
R 12252904929299 66 138/37521
R 12252904929299 66 139/38175
R 12252904929299 66 140/41930
R 24214294944371 82 141/45117
R 37592143853 66 142/46948
R 37592143853 66 143/47930
R 12252904929299 66 144/49351
R 638621868573 60 145/61220
R 638621868573 60 146/65223
R 37592143853 66 147/68376
R 638621868573 60 148/70169
R 638621868573 60 149/73685
R 638621868573 60 150/77167
R 638621868573 60 151/80961
R 638621868573 60 152/84012
R 638621868573 60 153/100101
R 638621868573 60 154/
R 638621868573 60 155/
R 638621868573 60 156/
R 638621868573 60 157/<150000
R 638621868573 60 158/164463
R 638621868573 60 159/169447
R 638621868573 60 160/195317
R 638621868573 60 161/202473
R 638621868573 60 162/233805
[/CODE]

Just a few minor records to post:

R 27838286939021 66 29/72
R 23249195384497 60 74/1009
R 23249195384497 60 77/1224
R 23249195384497 60 78/1286

I just finished the first 3 runs for n=75-100k, and again the record tables need to be rewritten:

S 16196964114523 58 [B]158/95487[/B] (p/ln(n) = [B]13.779[/B])
S 1323953181459703 100 154/98228 (13.397)
S 639141497343255 100 154/98742 (13.391)

[QUOTE=Thomas11;206542]I just finished the first 3 runs for n=75-100k, and again the record tables need to be rewritten:

S 16196964114523 58 [B]158/95487[/B] (p/ln(n) = [B]13.779[/B])
S 1323953181459703 100 154/98228 (13.397)
S 639141497343255 100 154/98742 (13.391)[/QUOTE]

OMG !!!!!!!! Sensational.

Do you want me to start sieving?

[QUOTE=robert44444uk;206545]
Do you want me to start sieving?[/QUOTE]

I already started a sieve for this and another few candidates.
Currently I'm testing a few more in the 75k-100k range and will switch to higher n once the sieve is ready.

Things can only get better:
S 1061615018040269 106 [B]159/99803[/B] (p/ln(n) = [B]13.813[/B]) :smile:

Who's next? 160/100000 anyone?

[QUOTE=Thomas11;206719]Things can only get better:
S 1061615018040269 106 [B]159/99803[/B] (p/ln(n) = [B]13.813[/B]) :smile:

Who's next? 160/100000 anyone?[/QUOTE]

This is totally great as it is an E(106)

This would give 176/350000 (level of checking for best to date), 191/1000000 and 200/1942000, so is a definite candidate for reaching the big goal.

[QUOTE=robert44444uk;206725]This is totally great as it is an E(106)

This would give 176/350000 (level of checking for best to date), 191/1000000 and 200/1942000, so is a definite candidate for reaching the big goal.[/QUOTE]

Well, since the weight p/ln(n) seems not to be a fixed number but gets larger with increasing n, there is a good chance to reach 200 PRPs much earlier.

A weight of 14 should be easily achievable for this candidate or the other within the interval n=100-150k...

[QUOTE=Thomas11;206727]Well, since the weight p/ln(n) seems not to be a fixed number but gets larger with increasing n, there is a good chance to reach 200 PRPs much earlier.

A weight of 14 should be easily achievable for this candidate or the other within the interval n=100-150k...[/QUOTE]

I agree the weight appears to increase, but that is also a factor of the types of superperformers we concentrate on. We ignore those whose p/ln(n) decrease!

Not sure about probabilities though.

You may be right. Lets hope so.

BTW I have gone back to looking at E52s, but I am only looking for those with 100/8000 - I want to find a small y in 100/y or a big x/10000. Setting the goal higher means that I am zooming through the 52s.

[QUOTE=Thomas11;206727]Well, since the weight p/ln(n) seems not to be a fixed number but gets larger with increasing n, there is a good chance to reach 200 PRPs much earlier.[/QUOTE]

In fact p/ln(n) approaches exactly the Nash weight as n goes to infinity.