Very Prime Riesel and Sierpinski k

[robert44444uk]

I'm not a programmer at all, so don't know if Robert G's software can be adjusted to do E28 to E37. Of course, you can always use Axn's software, which is known to be reliable,and which we used before Robert G's work.

The only issue there is the fact that Axn's software is not as efficient, maybe by a factor of 5 to 10 at finding VPS. But is perfectly adequate for smaller k targets. It is probably not the most efficient algorithm for searching for long CCs.

I do have the E28 and E37 Reisel racing records chart - no work was carried out on the Sierpinski side.

Regards

Robert

[Thomas11]

I have already considered some additional modifications to the program (e.g. adding the check whether a sequence is actually a member of a higher E level, automatic and optimal choice of Nash and Smith check parameters, etc.). And, perhaps, adding a graphical user interface, which would make it more attractive to potential new coworkers...

Right now, I'm not sure, if the algorithm can be easily changed for handling also E=28 and E=36. There are some hard-coded multipliers, which probably must changed.

Nevertheless, it's good to know that there is increasing interest in this program. This gives me some additional push forward...

[Thomas11]

Originally Posted by Thomas11

There was also a 116/10000 the same day:

S 144614850311421 60 100/5496 116/10000 K=1206288612570998158177981005 iteration=50 I=22614 Sun Mar 11 08:48:44 2012

I will start sieving them (together with some other 110+ sequences) this evening. Stay tuned...

Oh well, it turns out that this sequence is actually S 215814850311421 66, which I found already earlier.

But there is another noteworthy sequence in the news:

S 387050125955097 172 100/8526 105/10000

Actually the first S172!

[pinhodecarlos]

With the new enhance of having the possibility to stop the client at a given iteration/subiteration it is more easy to split the work into different clients. This means various co-workers can work with the same E therefore I think it is time to create a reservation table.

[Thomas11]

Originally Posted by robert44444uk

Before we receive more details of Thomas11's latest candidate...

Up to n=20,000 it produced 128 primes, which is the second best sequences at this level (after 134/20000 for the S66 found earlier)

And it set a few new absolute records, including a noteworthy 115/7000:

111 5954 216650161657053 S 58
112 6392 216650161657053 S 58
113 6395 216650161657053 S 58
114 6527 216650161657053 S 58
115 6907 216650161657053 S 58
116 8489 216650161657053 S 58

118 8998 216650161657053 S 58
119 9097 216650161657053 S 58
120 9805 216650161657053 S 58

122 11389 216650161657053 S 58

[robert44444uk]

Gosh page 17 of this thread suddenly.

Some more absolute Riesel records:

159 139973 440310850049907 R 82
160 143571 440310850049907 R 82

Three more for fresh territory on the Riesel side.

Congrats Thomas11 for all his new records!

[robert44444uk]

Originally Posted by Thomas11

Up to n=20,000 it produced 128 primes, which is the second best sequences at this level (after 134/20000 for the S66 found earlier)

And it set a few new absolute records, including a noteworthy 115/7000:

111 5954 216650161657053 S 58
112 6392 216650161657053 S 58
113 6395 216650161657053 S 58
114 6527 216650161657053 S 58
115 6907 216650161657053 S 58
116 8489 216650161657053 S 58

118 8998 216650161657053 S 58
119 9097 216650161657053 S 58
120 9805 216650161657053 S 58

122 11389 216650161657053 S 58

Don't think they are all absolute...but they are certainly Sierpinski records. My 121 Riesel candidate produced:

112 6159
113 6213
114 6218
115 6872
116 7388
117 7523
118 7600
119 7799
120 9283

But Mr Riesel concedes 111 and 122, where the best are 5996 and 12865 (from a E106 candidate)

Mr Riesel also claims one E66 at 128/19034

[Thomas11]

Encouraged by Gary's and Carlos' request I had a closer look into the source code. It turns out that it can be modified for E<52 quite easily.

Attached is a version for E>=36. There is a 32bit (for P4) and a 64bit binary (for Core2).

I did a few tests for the new code and it seems to work quite well.
And it already produced a nice Sierpinski VPS (maybe already known):

S 177693671 36 100/7398 106/10000 K=7770564667602165

Please note the following facts:
For E=36 I had to reduce the size of the CRT cycle. The cycle of the original code is based on the primes 7, 17, 23, 41, 47, 71, 79, and 97, whose product yields a cycle length of 2869549272527.
For E=36 we need to skip 79 and 97. This reduces the length of each cycle (iteration) to 374468129. This means that the iterations are much shorter now, and that there are only 3024 sub-iterations (I's) compared to 120960 for the original code.

The code should also work for higher E levels (52, 58, and the like).
But it will be significantly slower than the original code.

I will post another version (for E>=28) in a separate post.

Please do some tests and report about problems you may encounter.
Depending on your cpu power it would be nice if someone could verify at least one E>=52 VPS with the E=36 code...

[Thomas11]

And here comes the E>=28 variant.
The cycle length is again shorter, since we need to skip also p=71 (Ord2=35).
This results in a cycle length of 5274199 with only 84 sub-iterations (I) per iteration.

Again, this version will be slower than the E>=36 and the E>=52 variants.

Of course, in a future version we should combine all those variants (also for E=10/12) in one single executable. But we need to find a proper solution for distinguishing between the different iteration/I schemes (e.g. when running "one" iteration for E=52 which different cycle lengths).

[Thomas11]

I forgot to include the source code. So here it is...

[Thomas11]

And another milestone is reached:
There are now more than 10,000 known Sierpinski VPS!

Here is a little statistics:

	Total	M52	M58	M60	M66	M82	M100	M106	M130	M138	M148	M162	M172	M178	M180	M196	M210	M226
100	2683	580	659	316	637	118	167	105	69	17	13	0	0	2	0	0	0	0
101	2155	442	531	274	529	88	129	89	48	7	17	0	0	0	0	0	1	0
102	1770	339	436	211	502	62	101	68	32	6	13	0	0	0	0	0	0	0
103	1274	278	295	169	311	54	74	48	29	6	9	1	0	0	0	0	0	0
104	886	153	216	108	259	34	41	38	31	3	3	0	0	0	0	0	0	0
105	673	132	135	79	209	32	40	26	13	3	3	0	1	0	0	0	0	0
106	401	68	95	53	127	15	21	11	6	2	2	0	0	1	0	0	0	0
107	287	48	63	35	89	11	23	14	1	1	2	0	0	0	0	0	0	0
108	180	39	35	21	48	9	13	10	1	2	2	0	0	0	0	0	0	0
109	106	12	26	11	34	7	8	4	2	0	2	0	0	0	0	0	0	0
110	64	10	16	10	16	3	6	3	0	0	0	0	0	0	0	0	0	0
111	40	6	9	5	12	4	4	0	0	0	0	0	0	0	0	0	0	0
112	21	1	4	1	9	0	1	2	1	1	1	0	0	0	0	0	0	0
113	13	3	2	0	5	0	1	2	0	0	0	0	0	0	0	0	0	0
114	9	3	0	1	5	0	0	0	0	0	0	0	0	0	0	0	0	0
115	4	1	1	0	2	0	0	0	0	0	0	0	0	0	0	0	0	0
116	1	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0
117	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
118	1	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0
119	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
120	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
total:	10570	2116	2524	1294	2796	437	629	420	233	48	67	1	1	3	0	0	1	0

iterations:	58	70	32	80	52	2000	2290	3100	3100	6850	2435	600	285	660	1350	800	800
VPS/iter:	36.5	36.1	40.4	35.0	8.4	0.3	0.2	0.1	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0

Actually I have no explanation for the slightly higher outcome for E=60. Maybe this is due to different levels in the Smith check.