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

[/CODE]

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

[QUOTE=robert44444uk;378004]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[/QUOTE]

This should have read 182/212228

This candidate is now at 186/250000 with a further one discovered at a higher n.

[QUOTE=robert44444uk;378572]This should have read 182/212228

This candidate is now at 186/250000 with a further one discovered at a higher n.[/QUOTE]

I gave up on this after a long primeless gap after 189/273212 and tested up to 345000. It is still one of only two candidate with 180 primes or more.

I have been working on a very impressive larger candidate:

R 240767517392458807 178 110/10000 125/20000 146/50000 158/100000 171/198000

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*2^176883-1
3*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*139*149*163*383*2085094303*2^179172-1
3*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*139*149*163*383*2085094303*2^220027-1
3*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*139*149*163*383*2085094303*2^253731-1
3*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*139*149*163*383*2085094303*2^256104-1
3*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*139*149*163*383*2085094303*2^258454-1
3*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*139*149*163*383*2085094303*2^280583-1[/CODE]
It has now been tested to n=282642. It is no longer reserved by anyone, as far as I know.