k=22544089918041953*E(130) generates 216 known primes

Thomas11 · 2013-07-30, 17:17

Perhaps some of you may have noticed the recent progress in the Very Prime Riesel and Sierpinski k thread started by Robert Smith.

About one month ago Robert found a Riesel k, a so called VPS (Very Prime Series), for which we discovered 201 primes so far (up to n=480k).
This is quite extraordinary, since there are no other known series with 200 primes so far (actually no other series has 183 or more known primes).

Since our resources are limited we are offering this k to the RPS community.

The candidate is k=22544089918041953*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131 (=1480472640274704456611717878515654164205), a 40 digits number. Its Nash weight is 8818 (= "very high").

Now the unpleasant facts about this k:
~~LLR cannot handle such large values of k, therefore one has to use PFGW.~~
A single LLR test or a PRP test using PFGW typically takes 4-5 times as long as a LLR test for an "ordinary" k of 3-5 digits having the same n.

The attached file contains the range n=500-800k sieved up to p=6.34T, which should keep us busy for a while. Please help yourself to pick a suitable range for your machine(s).

Well, there would be no Top5000 credit for primes found in this range.
But with your help we could drive this k into the megabit range quite soon!

Status

Code:

      Range       Tested by        Status
      1-250,000 - Robert         - Complete (191 primes)
250,001-500,000 - Thomas         - Complete (14 primes)
500,001-600,000 - Lennart        - Complete (4 primes)
600,001-610,000 - Antonio        - Complete (2 primes)
610,001-612,000 - lsoule         - Complete
612,001-614,000 - Robert         - Complete
614,001-620,000 - lsoule         - Complete
620,001-630,000 - Batalov        - Complete
630,001-635,000 - Antonio        - Complete
635,001-640,000 - lsoule         - Complete (1 prime)
640,001-730,000 - Batalov        - Complete (1 prime)
730,001-732,000 - Kosmaj         - Complete
732,001-740,000 - lsoule         - Complete
740,001-742,000 - Antonio        - Complete
742,001-750,000 - lsoule         - Complete
750,001-770,000 - Thomas         - Complete
770,001-775,000 - Antonio        - Complete
775,001-780,000 - Trilo          - Complete
780,001-790,000 - lsoule         - Complete (1 prime)
790,001-792,000 - Robert         - Complete
792,001-810,000 - lsoule         - Complete
810,001-814,000 - Robert         - Complete
814,001-840,000 - lsoule         - Complete (1 prime)
840,001-842,000 - Robert         - Complete
842,001-880,000 - lsoule         - Complete
880,001-882,000 - Robert         - In Progress
882,001-890,000 - lsoule         - Complete
890,001-904,000 - lsoule         - Complete

1,000,001-1,030,000 - Batalov    - Complete (1 prime)

Input files (in the attached 22544.zip file):
22544mi790to800sv_6340B.txt ... pfgw input file in ABC format (790-800k)
22544mi800to1000sv_9600B.txt ... pfgw input file in ABC format (800-1000k)
llr_input_790to1000.txt ... LLR input file in NewPgen format (790-1000k)
llr_input_1030to1200.txt ... LLR input file in NewPgen format (1030-1200k)

robert44444uk · 2013-07-30, 17:30

I think it would be best to take 2,000 n blocks to begin with. For example 500-502.

I am just finishing off 228,000-250,000, and Thomas11 has a little bit to do in his range, and therefore there may be more than 201 primes at 500000.

firejuggler · 2013-07-30, 17:50

A test at n=500,000 take about 520 seconds, on a 2500K at stock clock.

Thomas11 · 2013-07-31, 07:53

This morning another prime (actually a PRP) popped up for n=496187.

202 primes now!

robert44444uk · 2013-07-31, 10:02

I have posted the discovery this morning on the Yahoo Primeform group, with a short history of the search.

http://tech.groups.yahoo.com/group/p.../message/11407

the primes found to date:

Code:

1     1
2     2
3     11
4     14
5     16
6     36
7     41
8     52
9     53
10    64
11    65
12    73
13    75
14    80
15    91
16    124
17    131
18    140
19    156
20    158
21    166
22    170
23    189
24    194
25    223
26    224
27    233
28    240
29    250
30    275
31    284
32    288
33    354
34    374
35    405
36    478
37    486
38    489
39    498
40    500
41    521
42    527
43    556
44    562
45    591
46    596
47    623
48    642
49    643
50    650
51    708
52    802
53    839
54    850
55    867
56    883
57    960
58    985
59    1003
60    1070
61    1108
62    1173
63    1207
64    1238
65    1276
66    1322
67    1361
68    1374
69    1375
70    1509
71    1570
72    1592
73    1636
74    1717
75    1720
76    1800
77    1808
78    1999
79    2150
80    2251
81    2352
82    2373
83    2550
84    2576
85    2596
86    2692
87    2697
88    2791
89    2956
90    3076
91    3178
92    3325
93    3590
94    4221
95    4327
96    4344
97    4385
98    4505
99    4585
100    4913
101    5217
102    5599
103    6478
104    6864
105    7089
106    7106
107    8140
108    8382
109    8528
110    8784
111    8787
112    9399
113    11069
114    11311
115    11853
116    14292
117    15198
118    15320
119    15825
120    15999
121    17570
122    17840
123    17887
124    17935
125    18401
126    20262
127    20460
128    20503
129    22568
130    22887
131    25002
132    26252
133    26523
134    27251
135    28233
136    29803
137    30173
138    31212
139    31424
140    32583
141    33696
142    36106
143    36320
144    40172
145    42457
146    44900
147    46170
148    46787
149    47920
150    49784
151    53246
152    55579
153    59638
154    60260
155    64574
156    67190
157    67470
158    71221
159    73142
160    77776
161    80678
162    84684
163    87557
164    96045
165    102231
166    102651
167    104202
168    104655
169    111235
170    111239
171    118689
172    119254
173    129630
174    134337
175    134490
176    141805
177    146149
178    159874
179    163330
180    168072
181    174712
182    177119
183    177684
184    190958
185    193804
186    197942
187    210616
188    226559
189    227776
190    229069
191    245288
192    255530
193    294807
194    318934
195    334623
196    334645
197    363020
198    376732
199    403709
200    414907
201    449150
202    472040
203    479697
204    496187
205    498496
206    517692
207    531133
208    549598
209    587833
210    608207
211    608462
212    639888
213    716611
214    788439
215    834442

216    1025897

Current total: 216 primes

robert44444uk · 2013-07-31, 12:57

The table I published is out of date again.

190 229069

That makes 203 primes to date

robert44444uk · 2013-07-31, 12:59

Quote:

Originally Posted by firejuggler

A test at n=500,000 take about 520 seconds, on a 2500K at stock clock.

Or 2.5 days per range of 2000 n, which has about 400 tests

firejuggler · 2013-07-31, 13:10

I'll do some work when I come back(mid august). Right now, my core are used.

Lennart · 2013-07-31, 18:10

Reserving
500,001-600,000 - Lennart

kar_bon · 2013-07-31, 18:34

I've updated my Riesel-Payam page with this record holder.

Thomas11 · 2013-07-31, 22:20

Another prime found: 204? 498496

250,001-500,000 completed (14 primes).

2013-07-31, 12:57	#6
robert44444uk Jun 2003 Suva, Fiji 2³·3·5·17 Posts	190th prime...203 overall The table I published is out of date again. 190 229069 That makes 203 primes to date

2013-07-31, 13:10	#8
firejuggler "Vincent" Apr 2010 Over the rainbow 2²×7×103 Posts	I'll do some work when I come back(mid august). Right now, my core are used. Last fiddled with by firejuggler on 2013-07-31 at 13:11

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2013-07-30, 17:30	#2
robert44444uk Jun 2003 Suva, Fiji 2040₁₀ Posts	I think it would be best to take 2,000 n blocks to begin with. For example 500-502. I am just finishing off 228,000-250,000, and Thomas11 has a little bit to do in his range, and therefore there may be more than 201 primes at 500000.

2013-07-30, 17:50	#3
firejuggler "Vincent" Apr 2010 Over the rainbow 5504₈ Posts	A test at n=500,000 take about 520 seconds, on a 2500K at stock clock.

2013-07-31, 07:53	#4
Thomas11 Feb 2003 2⁷·3·5 Posts	This morning another prime (actually a PRP) popped up for n=496187. 202 primes now!

2013-07-31, 18:10	#9
Lennart "Lennart" Jun 2007 1120₁₀ Posts	Reserving 500,001-600,000 - Lennart

2013-07-31, 18:34	#10
kar_bon Mar 2006 Germany 5667₈ Posts	I've updated my Riesel-Payam page with this record holder.

2013-07-31, 22:20	#11
Thomas11 Feb 2003 2⁷·3·5 Posts	Another prime found: 204? 498496 250,001-500,000 completed (14 primes).