mersenneforum.org k=22544089918041953*E(130) generates 216 known primes
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2013-07-30, 17:17   #1
Thomas11

Feb 2003

22·32·53 Posts
k=22544089918041953*E(130) generates 216 known primes

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)
Attached Files
 22544.zip (302.3 KB, 110 views)

Last fiddled with by Thomas11 on 2015-02-10 at 08:39

 2013-07-30, 17:30 #2 robert44444uk     Jun 2003 Oxford, UK 111100011012 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     Apr 2010 Over the rainbow A0416 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 22×32×53 Posts This morning another prime (actually a PRP) popped up for n=496187. 202 primes now!
 2013-07-31, 10:02 #5 robert44444uk     Jun 2003 Oxford, UK 1,933 Posts 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 Last fiddled with by Batalov on 2014-02-06 at 18:00 Reason: Table updated after new primes were found.
 2013-07-31, 12:57 #6 robert44444uk     Jun 2003 Oxford, UK 111100011012 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, 12:59   #7
robert44444uk

Jun 2003
Oxford, UK

1,933 Posts

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

 2013-07-31, 13:10 #8 firejuggler     Apr 2010 Over the rainbow 22×641 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
 2013-07-31, 18:10 #9 Lennart     "Lennart" Jun 2007 25·5·7 Posts Reserving 500,001-600,000 - Lennart
 2013-07-31, 18:34 #10 kar_bon     Mar 2006 Germany 33·107 Posts I've updated my Riesel-Payam page with this record holder.
 2013-07-31, 22:20 #11 Thomas11     Feb 2003 77416 Posts Another prime found: 204? 498496 250,001-500,000 completed (14 primes).

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