Very Prime Riesel and Sierpinski k

[robert44444uk]

I looked at some of Jarek's best Riesels - there are some gems that are being taken to higher levels, but the best of the lot:

R 50013530105764248915 60 100/5084 122/10000 146/37900
and counting

[robert44444uk]

Originally Posted by robert44444uk

I looked at some of Jarek's best Riesels - there are some gems that are being taken to higher levels, but the best of the lot:

R 50013530105764248915 60 100/5084 122/10000 146/37900
and counting

157/75000 - will continue with this one

[robert44444uk]

Originally Posted by robert44444uk

157/75000 - will continue with this one

And now 161/107700. There was a large gap between the prime at 66052 and 95621 which is a real shame.

This candidate is the easily the second best Riesel at 161/103309, but 5 primes behind the leader.

[Trilo]

Any finds with the 100th prime below 3000 yet?

[Jarek]

Originally Posted by Trilo

Any finds with the 100th prime below 3000 yet?

No. I have seven 98/3000 and nothing higher.
You can see all 95/3000 and higher found during my current search in the directory
http://www.math.uni.wroc.pl/~p-k1g4/VPS/?C=M;O=D
file all95@3K.txt

This file is being updated whenever I look at the results.

[robert44444uk]

Originally Posted by Jarek

No. I have seven 98/3000 and nothing higher.
You can see all 95/3000 and higher found during my current search in the directory
http://www.math.uni.wroc.pl/~p-k1g4/VPS/?C=M;O=D
file all95@3K.txt

This file is being updated whenever I look at the results.

To avoid duplication I am in the latter stages of taking all of Jarek's finds, posted as 88@3K-1 and 88@3K-2 to at least 10K.

There are a couple of new 120+/10000 so far in the batch, the best of which is 125/10000, equal to the record. There are over 20 with 115+

R 54111151145860262601 60 100/4307 125/10000 135/20000 141/30000 144/67756 - stopped
R 59654515826093904233 58 100/4287 122/10000 133/20000 138/30000 - stopped

Checking lower down, one of the longest standing records has been 74/1000, but two Sierpinskis, quite "close" to each other in terms of k value, produced 75/1000

S 75807413108261155157 60 75/1000 109/10000
S 73489559227095936793 60 75/1000 105/10000

[robert44444uk]

Originally Posted by robert44444uk

And now 161/107700. There was a large gap between the prime at 66052 and 95621 which is a real shame.

This candidate is the easily the second best Riesel at 161/103309, but 5 primes behind the leader.

I ended this search at 169 primes

R 50013530105764248915 60 100/5084 122/10000 159/100000 169/187260

[Jarek]

Finally, I just got it !!!
R 1640793485632684817 100 100/3000

[robert44444uk]

Originally Posted by Jarek

Finally, I just got it !!!
R 1640793485632684817 100 100/3000

Very many congratulations, Jarek. A major find.

I will take this one up to see how it performs

[robert44444uk]

Originally Posted by Jarek

Finally, I just got it !!!
R 1640793485632684817 100 100/3000

Actually this was 100/2570, blowing the record away!

Other astounding stats, it was only 69/1000, but 80/1190! It got to 119/10000 so not the best, but still very robust with 125/13000

[robert44444uk]

I finally got to take all of Jarek's 6,664 candidates at 88 or more at 3K up to 10K, and then to take all those at 114 or more to 20K

I can't post all of the results for obvious reasons, but in general, all records have been blown away and it will take a long time before I can construct the records table. There are on average 10 or more candidates that beat the Riesel records at any level of n between 1000 and 20000.

A list of those that are 130 or more at 20K (and 114 or more at 10K) is shown below, I have already started taking most of these up to 50K.

In this post are the stars, in the next some statistics

S/R	M	y	10K	20K
S	53x61	5254406290016627149	119	136
R	61	54111151145860262601	125	135
S	67	132874844545926904079	120	135
R	59	59654515826093904233	122	133
R	53	52052849362908139779	117	133
R	83	12204165318496075939	115	133
R	61	50013530105764248915	122	132
R	53	23971910160715957653	121	132
R	101	25747131124396625929	120	132
R	101	1640793485632684817	119	132
R	61	21392794569384899731	116	132
S	67	21673540652538543435	116	132
S	53x61	2435424994198853557	116	132
S	59	3735959948688708639	115	132
S	61	25320576989821784981	125	131
S	83	77768053610557101865	123	131
S	61	26510864838669015851	120	131
R	67	37905278470968590827	119	131
S	61	32876350375831499005	118	131
R	67	36638805119351662083	117	131
S	67	47176934193180632513	117	131
S	101	42564402345755029091	117	131
R	59x67	49817171332553543619	116	131
S	83	12579662575136809647	116	131
S	101	124551114605314947	116	131
S	61	33408563159599168199	115	131
S	83	137659329089344149093	115	131
R	59x67	33967996189713657281	114	131
S	67	29980027676153940091	114	131
S	53	28701065754597860047	119	130
S	61	29782704902101681187	119	130
S	101	15596237216944427549	118	130
R	67	25251715839199933629	117	130
R	101	52889672364117448319	117	130
S	61	19110518425938234561	117	130
S	59	10478622225841902593	116	130
R	61	68995088315679886437	115	130
R	101	7970728737809036685	115	130
S	59x67	12639966463444216893	115	130
R	59	64633568438922733131	114	130