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

Perhaps some of you may have noticed the recent progress in the [URL="http://www.mersenneforum.org/showthread.php?t=9755"]Very Prime Riesel and Sierpinski k thread[/URL] started by Robert Smith.

About one month ago Robert found a Riesel k, a so called VPS (Very Prime Series), for which we discovered [B]201 primes[/B] 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 [B]k=22544089918041953*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131[/B] (=1480472640274704456611717878515654164205), a 40 digits number. Its [B]Nash weight is 8818[/B] (= "very high").

Now the unpleasant facts about this k:
[STRIKE]LLR cannot handle such large values of k, therefore one has to use PFGW.[/STRIKE]
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!

[B]Status[/B]
[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)
[/CODE]

[B]Input files[/B] (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)

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.

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

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

[B]202 primes[/B] now!

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

[URL]http://tech.groups.yahoo.com/group/primeform/message/11407[/URL]

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
[/CODE][B]Current total: 216 primes[/B]

190th prime...203 overall
 

The table I published is out of date again.

[B]190 229069[/B]

That makes 203 primes to date

[QUOTE=firejuggler;347787]A test at n=500,000 take about 520 seconds, on a 2500K at stock clock.[/QUOTE]

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

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

Reserving
500,001-600,000 - Lennart

I've updated my [url=http://www.rieselprime.de/Related/RieselPayam.htm]Riesel-Payam page[/url] with this record holder.

Another prime found: [B]204? 498496[/B] :smile:

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