20140713, 11:58  #584 
Jun 2003
Oxford, UK
2×953 Posts 
Here are basis statistics around the prime counts for the 6,664 candidates at 10K. 6,279 of the were VPS. An astonishing 1,362 were 110 or more, and 11 at 120 or more.
The 339 at 114 or more have been taken to 20K and beyond. Code:
primes #candidates Cumul 90 1 91 0 6663 92 1 6663 93 0 6662 94 9 6662 95 11 6653 96 39 6642 97 46 6603 98 99 6557 99 179 6458 100 275 6279 101 340 6004 102 464 5664 103 496 5200 104 614 4704 105 591 4090 106 609 3499 107 569 2890 108 515 2321 109 444 1806 110 358 1362 111 292 1004 112 218 712 113 155 494 114 123 339 115 87 216 116 54 129 117 40 75 118 13 35 119 11 22 120 4 11 121 2 7 122 2 5 123 1 3 124 0 2 125 2 2 6664 Last fiddled with by robert44444uk on 20140713 at 11:59 
20140713, 12:05  #585 
Jun 2003
Oxford, UK
2·953 Posts 
While I have been working on Jarek's candidates, I also have some news from my own Riesel search. This candidate beats a number of records at the higher levels, and it is by no means certain that any of Jarek's candidates will do better than this. It has fallen a little behind the record but is the second Riesel for which more than 180 primes is known.
R 28201354278197625 100 118/10000 131/20000 155/50000 170/100000 182/221228 Last fiddled with by robert44444uk on 20140713 at 12:06 
20140719, 08:42  #586  
Jun 2003
Oxford, UK
1906_{10} Posts 
Quote:
This candidate is now at 186/250000 with a further one discovered at a higher n. 

20140801, 17:22  #587  
Jun 2003
Oxford, UK
11101110010_{2} Posts 
Quote:
I have been working on a very impressive larger candidate: R 240767517392458807 178 110/10000 125/20000 146/50000 158/100000 171/198000 

20161113, 15:26  #588 
Sep 2010
Scandinavia
3·5·41 Posts 
3*383*2085094303*M(163)
Here are some new primes for one of the candidates listed on Karsten's site:
Code:
3*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*139*149*163*383*2085094303*2^1768831 3*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*139*149*163*383*2085094303*2^1791721 3*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*139*149*163*383*2085094303*2^2200271 3*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*139*149*163*383*2085094303*2^2537311 3*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*139*149*163*383*2085094303*2^2561041 3*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*139*149*163*383*2085094303*2^2584541 3*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*139*149*163*383*2085094303*2^2805831 
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