Very Prime Riesel and Sierpinski k

[Thomas11]

I'm very impressed about our "star" 13330...M148!
That's really amazing! Let's see if we could find another (better) one which would hit the 150/100000...

Meanwhile I've generated another 531 Sierpinski VPS for E=52...138 (no new M148 yet). You will find them in the attached file. Note, that 8 of them (the y values) have higher E+1 factors and become therefore members of the next higher sequence (indicated in the file). 6 of them are already known. So, strictly speaking, "only" 525 are new VPS.

For the moment I will take the following one further:
S 732478130807511 106 100/4930 112/10000

All others are open for anybody else...

[henryzz]

reserving S 12034494960083 66 100/6932 112/10000 from thomas' latest file to take further

[robert44444uk]

Originally Posted by Thomas11

Meanwhile I've generated another 531 Sierpinski VPS for E=52...138 (no new M148 yet).

Riches indeed. Takes us to 2000 !!!!

The most interesting fact in this batch is the large number of E100 and E106 which are 105/10000 and better.

E	VPS	105+	105+/VPS
52	82	7	8.5%
58	88	9	10.2%
60	58	5	8.6%
66	89	3	3.4%
82	71	4	5.6%
100	65	10	15.4%
106	51	5	9.8%
130	23	0	0.0%
138	4	1	25.0%

[robert44444uk]

Originally Posted by robert44444uk

Riches indeed. Takes us to 2000 !!!!

Not quite, but here are frequencies:

	R+S	52	58	60	66	82	100	106	130	138	148
											
100	551	103	109	78	96	68	42	34	14	6	1
101	421	76	84	64	92	50	22	19	12	1	1
102	297	38	67	47	66	32	25	13	7	0	2
103	235	40	50	32	45	24	19	15	9	1	0
104	160	25	24	25	48	14	8	7	7	1	1
105	112	18	19	16	21	16	7	9	5	1	0
106	83	12	19	9	23	7	5	4	2	1	1
107	50	7	13	7	10	1	7	3	0	1	1
108	26	7	3	4	1	2	3	5	1	0	0
109	17	1	4	3	5	0	2	1	1	0	0
110	10	0	2	4	2	1	0	1	0	0	0
111	8	1	3	0	0	3	1	0	0	0	0
112	5	0	0	0	2	0	1	1	0	0	1
113	1	0	0	1	0	0	0	0	0	0	0
114	0	0	0	0	0	0	0	0	0	0	0
115	1	0	1	0	0	0	0	0	0	0	0
116	0	0	0	0	0	0	0	0	0	0	0
											
	1977	328	398	290	411	218	142	112	58	12	8

[robert44444uk]

Originally Posted by robert44444uk

13330...M148 now at 147/96228.

146/79804 and 147/94911 are both Sierpinski best. Need 148 to appear by n=97637. Does not look likely to hit 150/100000 which is a shame

Temporarily halted at 147/97816

[Thomas11]

Originally Posted by robert44444uk

13330...M148 now at 147/96228.

146/79804 and 147/94911 are both Sierpinski best. Need 148 to appear by n=97637. Does not look likely to hit 150/100000 which is a shame

This is just a first status report on 73247...M106. It's currently tested up to about n=62000 and it already reached 147 primes (PRPs) at this level!
So, if 13330...M148 was going like a train, this one is like a jet airliner!

Here are the counts:
S 732478130807511 106 100/4930 112/10000 128/20000 135/30000 140/50000 147/60000

Will most probably hit the 150/100000.

[robert44444uk]

Originally Posted by Thomas11

This is just a first status report on 73247...M106. It's currently tested up to about n=62000 and it already reached 147 primes (PRPs) at this level!
So, if 13330...M148 was going like a train, this one is like a jet airliner!

Here are the counts:
S 732478130807511 106 100/4930 112/10000 128/20000 135/30000 140/50000 147/60000

Will most probably hit the 150/100000.

Chaglassian/ Carmody reported the one Riesel at 149/<75000 , 152/<84013 and 157/<150000 but I do not have the primes between 134/29866 and 158/164463

This is a E106 so should do a lot better. Hope it beats these benchmarks. Worth posting the prps for n>10000 so that we can keep the records up to date.

[Thomas11]

Originally Posted by Thomas11

Will most probably hit the 150/100000.

Meanwhile it hit the 150th prime at n=75625. A little bit higher than expected, as there was a huge primeless gap between n=60000 and 70000.

Will continue this k up to at least n=100000...

For the statistics, here is the complete list of n for which 732478130807511*M106*2^n+1 is prime (PRP):
n=5, 20, 23, 25, 33, 36, 43, 45, 52, 53, 57, 67, 79, 80, 96, 98, 104, 109, 117, 126, 130, 132, 150, 174, 186, 203, 216, 227, 236, 241, 242, 252, 254, 258, 276, 277, 291, 295, 296, 301, 311, 319, 329, 334, 378, 388, 399, 427, 456, 458, 487, 531, 575, 594, 625, 677, 693, 728, 762, 824, 865, 898, 953, 1021, 1099, 1112, 1198, 1210, 1216, 1223, 1385, 1390, 1471, 1591, 1797, 1820, 1902, 1918, 2054, 2111, 2164, 2186, 2360, 2376, 2605, 2707, 2758, 2873, 2942, 3141, 3178, 3298, 3582, 3770, 4276, 4310, 4312, 4363, 4444, 4930, 4981, 5043, 5053, 5062, 5257, 6060, 6129, 6358, 6410, 7049, 7768, 9646, 10043, 10124, 11261, 11312, 11554, 12566, 13548, 14351, 14612, 15240, 15405, 16331, 17182, 17929, 19182, 19883, 21811, 21832, 22591, 24189, 25264, 26600, 26926, 34642, 36366, 36622, 40919, 43437, 51251, 54643, 55911, 56583, 56620, 57966, 59441, 70148, 71777, 75625 (150 PRPs)

[robert44444uk]

I now have over 700 new Riesel VPS. This week found 1 at 111, 1 at 109, 2 at 107, 2 at 106 and 1 at 105/10000

Will continue to find all Riesel VPS from E52 to E100

I am wondering if it makes sense to consider only targeting 105 and over by resetting the in.txt file to this higher barrier level. This might speed up the search as prp testing will not take up as much time.

I will investigate what the appropriate smith_check parameters for each E level

[Thomas11]

During the weekend I found only two new PRPs for 73247...M106:
n=105267 and n=107950. So in total there are 152 PRPs now.
Note the huge gap between n=75000 and 105000, which is a shame...

Originally Posted by robert44444uk

I am wondering if it makes sense to consider only targeting 105 and over by resetting the in.txt file to this higher barrier level. This might speed up the search as prp testing will not take up as much time.

It might be useful for the smaller ones, e.g. E=52, 58, 66, and perhaps 82, to set the target to 105/10000. However, for E=100 and higher, where the VPSs are quite rare, we should keep the target at 100/10000.

BTW.: I'm currently working on an automated procedure using Phil Carmody's ksieve and PFGW. The goal is to sieve about 40-50 candidates in parallel and then pipe them through PFGW. However, since the whole procedure consists of multiple shell and perl scripts, this will be restricted to Linux.

[robert44444uk]

Originally Posted by Thomas11

During the weekend I found only two new PRPs for 73247...M106:
n=105267 and n=107950. So in total there are 152 PRPs now.
Note the huge gap between n=75000 and 105000, which is a shame...

Shame, but watch..it will be like London buses, more will come along. BTW there is a huge PFGW penalty around n=160000, so suggest that is the upper limit unless it is a true record breaker at that level.

Originally Posted by Thomas11

BTW.: I'm currently working on an automated procedure using Phil Carmody's ksieve and PFGW. The goal is to sieve about 40-50 candidates in parallel and then pipe them through PFGW. However, since the whole procedure consists of multiple shell and perl scripts, this will be restricted to Linux.

OK cannot contribute to this, only Windoze here. However the idea is very efficient. Maybe Henryzz can contribute?