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-   -   Post small primes and tell us about your progress here (https://www.mersenneforum.org/showthread.php?t=2150)

Kosmaj 2004-02-27 07:02

Post small primes and tell us about your progress here
 
Well, there is no thread to post small primes of reserved k's
so I decided to create a new thread.

For my k=3611911875 up to n=100800 I found additional small primes for following n's:
75088
90363
91405
93732 <-- 100th prime
97888

There are now 101 primes to 100k and 6 primes in the 134-200k range. I'll continue the work in the 100-134k range and I just began tests in the 200-220 range. I sieved candidates in the 200-400 range to 800 bn using ksieve.

cyrix 2004-03-16 19:46

Ok, I searched up my k=158823815 up to n=85000 (and a little beyond this moment). While doing this I found 110 primes:

1, 3, 4, 7, 11, 12, 16, 19, 21, 28, 31, 40, 47, 53, 62, 69, 75, 76, 82, 98, 103, 104, 115, 118, 134, 151, 152, 154, 163, 177, 257, 261, 271, 274, 309, 328, 331, 349, 410, 452, 526, 573, 597, 616, 700, 714, 738, 862, 922, 923, 1009, 1025, 1306, 1564, 1848, 1936, 2032, 2061, 2074, 2212, 2255, 2467, 2522, 2627, 2678, 2753, 2788, 3011, 3979, 4185, 4983, 5189, 5494, 5850, 6838, 7076, 7469, 7816, 8048, 8226, 8396, 8624, 8738, 12933, 13540, 15779, 17388, 18792, 20849, 21382, 21446, 22330, 23681, 24527, 27299, 28409, 32634, 33558, 35264, 38374, 45234, 52257, 55111, 56096, 64593, 70900, 73506, 75326, 75617, 85535


With the other prime for n=336542 this makes 111 primes found for this k.

Cyrix

cyrix 2004-03-16 21:53

Oh, a typing error: Actual k=1581823815.
Cyrix

Kosmaj 2004-03-17 01:31

Then this is now our "best [I]k[/I]" since the 100th prime occured for n=38374. The previous best was k=2995125705, and i(100)=60190.

BotXXX 2004-03-19 08:09

I tested the 15k = 968911515 from n=2 to n=50000 and found the following primes. I will [b]not[/b] continue testing this 15k.
[code]
968911515 3
968911515 6
968911515 13
968911515 15
968911515 16
968911515 18
968911515 21
968911515 23
968911515 28
968911515 31
968911515 32
968911515 39
968911515 40
968911515 43
968911515 54
968911515 63
968911515 70
968911515 71
968911515 74
968911515 84
968911515 88
968911515 92
968911515 100
968911515 110
968911515 128
968911515 136
968911515 139
968911515 151
968911515 203
968911515 218
968911515 223
968911515 238
968911515 248
968911515 253
968911515 321
968911515 349
968911515 356
968911515 362
968911515 374
968911515 507
968911515 533
968911515 572
968911515 952
968911515 970
968911515 993
968911515 1037
968911515 1262
968911515 1373
968911515 1378
968911515 1408
968911515 1601
968911515 1602
968911515 1615
968911515 1985
968911515 2338
968911515 2955
968911515 3111
968911515 3170
968911515 3828
968911515 4171
968911515 4857
968911515 5646
968911515 7035
968911515 8861
968911515 9331
968911515 11432
968911515 13846
968911515 15273
968911515 15638
968911515 27221
968911515 28197
968911515 34579
968911515 40628
968911515 42459
968911515 45364
968911515 46492
968911515 46632
[/code]

BotXXX 2004-03-19 11:59

I also tested the 15k = 475977645 from n=2 to n=50000 and found the following primes. I will [b]not[/b] continue testing this 15k.
[code]
475977645 3
475977645 6
475977645 7
475977645 21
475977645 23
475977645 28
475977645 34
475977645 37
475977645 46
475977645 54
475977645 59
475977645 67
475977645 75
475977645 81
475977645 96
475977645 99
475977645 101
475977645 107
475977645 112
475977645 114
475977645 123
475977645 138
475977645 153
475977645 171
475977645 215
475977645 233
475977645 389
475977645 421
475977645 463
475977645 595
475977645 652
475977645 793
475977645 821
475977645 952
475977645 970
475977645 1167
475977645 1669
475977645 1899
475977645 1967
475977645 2025
475977645 2217
475977645 2254
475977645 2260
475977645 3059
475977645 3118
475977645 3787
475977645 4828
475977645 5352
475977645 6049
475977645 6544
475977645 6675
475977645 6676
475977645 6685
475977645 6915
475977645 7266
475977645 7868
475977645 8659
475977645 9040
475977645 9382
475977645 9584
475977645 9990
475977645 10146
475977645 10192
475977645 10757
475977645 11492
475977645 11788
475977645 12181
475977645 12430
475977645 12838
475977645 13878
475977645 14478
475977645 14691
475977645 14754
475977645 15460
475977645 16729
475977645 17037
475977645 18310
475977645 22465
475977645 23662
475977645 37615
475977645 41087
475977645 41827
475977645 43860
475977645 44640
[/code]

lsoule 2005-01-06 18:55

Here are the first 79 primes for 515106735. I'll continue searching to
see where the 100th prime occurs.

515106735 4
515106735 5
515106735 27
515106735 38
515106735 40
515106735 62
515106735 63
515106735 66
515106735 67
515106735 70
515106735 89
515106735 99
515106735 114
515106735 139
515106735 152
515106735 158
515106735 185
515106735 189
515106735 222
515106735 269
515106735 272
515106735 297
515106735 341
515106735 387
515106735 394
515106735 483
515106735 534
515106735 559
515106735 640
515106735 659
515106735 683
515106735 686
515106735 724
515106735 760
515106735 794
515106735 830
515106735 854
515106735 1121
515106735 1183
515106735 1314
515106735 1383
515106735 1427
515106735 1474
515106735 1521
515106735 1806
515106735 1896
515106735 2001
515106735 2092
515106735 2111
515106735 2282
515106735 2634
515106735 2737
515106735 3221
515106735 3343
515106735 4079
515106735 4137
515106735 4963
515106735 5086
515106735 5279
515106735 5567
515106735 6171
515106735 6623
515106735 10702
515106735 13178
515106735 14129
515106735 16075
515106735 16110
515106735 17041
515106735 18006
515106735 19518
515106735 21961
515106735 23612
515106735 26781
515106735 27811
515106735 29367
515106735 47173
515106735 58301
515106735 58722
515106735 61684

lsoule 2005-01-21 16:04

First hundred primes for 860541825
 
Here are the first hundred primes for 860541825.
The 100th occurs at n=54696
[QUOTE]
860541825 1
860541825 2
860541825 3
860541825 7
860541825 8
860541825 16
860541825 19
860541825 24
860541825 41
860541825 43
860541825 44
860541825 47
860541825 48
860541825 53
860541825 76
860541825 87
860541825 89
860541825 108
860541825 114
860541825 128
860541825 131
860541825 141
860541825 145
860541825 148
860541825 155
860541825 173
860541825 180
860541825 197
860541825 213
860541825 220
860541825 241
860541825 243
860541825 277
860541825 286
860541825 302
860541825 331
860541825 341
860541825 447
860541825 467
860541825 509
860541825 574
860541825 598
860541825 628
860541825 684
860541825 734
860541825 786
860541825 820
860541825 823
860541825 827
860541825 872
860541825 929
860541825 946
860541825 950
860541825 976
860541825 1067
860541825 1246
860541825 1405
860541825 1613
860541825 1712
860541825 1890
860541825 1939
860541825 2036
860541825 2105
860541825 2226
860541825 2630
860541825 2936
860541825 3151
860541825 3905
860541825 4324
860541825 4595
860541825 4891
860541825 5802
860541825 7355
860541825 7754
860541825 7805
860541825 8167
860541825 8915
860541825 11184
860541825 11755
860541825 12043
860541825 12999
860541825 13004
860541825 14180
860541825 15044
860541825 16155
860541825 16664
860541825 17447
860541825 18042
860541825 18811
860541825 21810
860541825 26177
860541825 27377
860541825 27632
860541825 30495
860541825 30498
860541825 34180
860541825 34347
860541825 40104
860541825 54696
[/QUOTE]

lsoule 2005-03-10 23:06

[FONT=Arial]After looking at Primoproths and Payam numbers, I'm now running a script
to see how many primes are generated for k's constructed by multiplying
all combinations of the first 11 primes. The top 20 so far are listed below
and ALL fall into the 15*k category. Some have primes listed on the
top-5000 site but some do not. Was something like this run to
generate the original 15k candidate list?

Format: #primes for n=1-10000, k
60 29058315
60 842691135
61 19635
61 25935
61 102765
61 15935205
61 3457939485
61 47912205
61 8580495
62 10015005
62 10555545
62 16545165
62 2330445
62 373065
63 111546435
64 14637315
64 25634895
65 190285095
66 26565
68 49335

thanks,
Larry

masser 2005-03-11 16:35

I believe the original 15k candidate list was produced by calculating the weights of all k divisible by 15 up to a certain limit and removing all of those k's with a weight lower than some cutoff.

There is a program available online called psieve that will compute the weights of a sequence of k values. You should check it out...

regards,
masser

lsoule 2005-03-16 21:46

Here are the first 100 primes for 8331405

8331405 9
8331405 11
8331405 17
8331405 21
8331405 31
8331405 32
8331405 33
8331405 45
8331405 57
8331405 61
8331405 64
8331405 67
8331405 69
8331405 77
8331405 80
8331405 85
8331405 88
8331405 107
8331405 115
8331405 117
8331405 120
8331405 121
8331405 124
8331405 147
8331405 155
8331405 161
8331405 164
8331405 168
8331405 177
8331405 179
8331405 221
8331405 232
8331405 258
8331405 261
8331405 264
8331405 281
8331405 282
8331405 299
8331405 308
8331405 342
8331405 415
8331405 471
8331405 503
8331405 504
8331405 505
8331405 537
8331405 572
8331405 680
8331405 989
8331405 1328
8331405 1565
8331405 1607
8331405 1613
8331405 1841
8331405 1953
8331405 2509
8331405 2692
8331405 2739
8331405 2834
8331405 3627
8331405 3735
8331405 3870
8331405 3960
8331405 4083
8331405 4682
8331405 4788
8331405 5187
8331405 5247
8331405 5623
8331405 5804
8331405 6015
8331405 6020
8331405 6405
8331405 6569
8331405 7052
8331405 7315
8331405 7477
8331405 7489
8331405 8389
8331405 8800
8331405 10407
8331405 10512
8331405 12035
8331405 13015
8331405 14634
8331405 14941
8331405 16339
8331405 16367
8331405 16554
8331405 26533
8331405 28153
8331405 29081
8331405 30222
8331405 32391
8331405 36371
8331405 37323
8331405 39251
8331405 43935
8331405 45052
8331405 45773

Kosmaj 2005-03-16 22:40

Larry,
8331405*2-1 = 16662809 is also prime.

Thus, the 100th prime occurs for n=45052 while in this respect the best among "old" candidates is k=1581823815 where the 100th prime occurs for n=38374. Very close! More such results can be found [URL=http://www.15k.org/stats.htm]here[/URL].

robert44444uk 2005-03-16 23:45

100 primes
 
For the groups interest, the best +1 number to get to a hundred primes got there with n=3258 with k = 1108828374241*M(59), where M(59) is a certain multiple of small primes p up to 59, excluding those with order base 2 of less than p-1. This is a Payam number, par excellence.

It may well be that the - series produced better, but I don't know for sure. In any case there are better numbers out there, although Phil Carmody thought that this was close to the ideal number at to that (i.e. 100 primes) range.

For your interest, this number was checked up to n=100000 with "only" 140 primes, so we stopped checking it in earnest - ther are plenty with greater than that at that level, but software does not allow for fast checking of theses k, because k is rather large.

Regards

Robert Smith

Ps this series is prime at n= (note the huge gap at 4495-7544)

3
11
13
14
18
19
23
25
26
29
31
42
45
50
64
65
71
86
98
101
116
119
134
191
194
195
212
257
259
269
276
284
285
294
307
324
396
403
406
420
447
449
459
480
486
540
545
602
607
625
654
659
703
742
780
827
828
838
848
867
923
960
976
982
1005
1011
1021
1037
1049
1081
1100
1130
1145
1192
1254
1327
1427
1488
1548
1599
1647
1663
1684
1818
1844
1861
1880
1892
1946
1951
1971
2044
2130
2150
2227
2328
2393
3215
3224
3258 no 100
3289
3405
3436
3450
3722
3833
4172
4227
4337
4495
7544
8666
9037
9263
9758
10493
10628
12817
12959
15351
15762
16529
18995
19249
21117
22601
25769
27486
32648
33107
38099
40751
52586
53046
53060
53105
54241
60535
75013
85111
102912
126708

robert44444uk 2005-03-16 23:49

n=10000
 
PS A good count for primes at 10000, on the + side would be greater than 116. The candidate at that level was 2158430601663 *M(67), whose 116th prime is at n=9971

Regards

Robert Smith

gribozavr 2005-04-17 09:06

Primes for 15k=187466565 with n from 1 to 100000
 
Here are primes I've found for 15k=187466565 with n from 1 to 100000:
[CODE]187466565 7
187466565 8
187466565 11
187466565 13
187466565 25
187466565 26
187466565 36
187466565 42
187466565 43
187466565 44
187466565 49
187466565 54
187466565 57
187466565 61
187466565 73
187466565 78
187466565 81
187466565 95
187466565 97
187466565 99
187466565 125
187466565 128
187466565 129
187466565 137
187466565 159
187466565 167
187466565 187
187466565 189
187466565 224
187466565 234
187466565 235
187466565 320
187466565 395
187466565 440
187466565 491
187466565 546
187466565 561
187466565 602
187466565 621
187466565 684
187466565 694
187466565 703
187466565 788
187466565 803
187466565 1158
187466565 1298
187466565 1422
187466565 1561
187466565 1727
187466565 1920
187466565 1946
187466565 2265
187466565 2675
187466565 2990
187466565 2994
187466565 3150
187466565 3296
187466565 3453
187466565 3525
187466565 3608
187466565 4006
187466565 4391
187466565 4688
187466565 4866
187466565 6842
187466565 6996
187466565 7014
187466565 7115
187466565 7393
187466565 7796
187466565 8505
187466565 9722
187466565 10587
187466565 11144
187466565 13574
187466565 13629
187466565 13793
187466565 13837
187466565 14678
187466565 15213
187466565 16210
187466565 16578
187466565 17355
187466565 19121
187466565 20215
187466565 21542
187466565 22635
187466565 28375
187466565 37256
187466565 41362
187466565 41785
187466565 41888
187466565 63163
187466565 65203
187466565 74889
187466565 78879
187466565 80097
187466565 92598[/CODE]
I will continue testing this 15k with n up to 200000.

VBCurtis 2005-04-21 03:46

Primes for k=3803443215:
n=1 through n=9 already on 15k.org site.
19,20,28 (PRPs), 53,56,58,112,235,313,339,367,372,376,397,413,454,525,543,576,
847,850,1027,1048,1061,1125,1160,1301, 1318, 1329,1503,1874,
2033,2536,2544,2553,2709,2953,3352,3649,3726,3887,4709,5075,
5167,5175,7092,10902,11933,12333,19168,19822,20276,21919,
22792,23567,24845,25793,39906,40936,42092,42258,51165,66033,
71287,72993,85641,90943,119027,159420,161247,167492,169409,
178053. 82 primes so far.
I'm at roughly n=188000 currently, planning to process to n=250,000, then decide whether to push the low-weight number beyond 1M or this number to higher powers.
What's the current cutoff for top-5000 entry? n=220,000?
-Curtis

lsoule 2005-04-21 04:06

The top-5000 cutoff is just below n=189,000 now.

-Larry

gribozavr 2005-04-25 18:47

Primes for 15k=187466565 with n from 100000 to 150000
 
The range 100000-150000 was sieved by me, gribozavr, and LLR'ed mostly by my friend yasya. :bow: So, please, give us both a credit for theese primes (write something like gribozavr and yasya): :banana:
[CODE]187466565 107376
187466565 109098
187466565 111081
187466565 127062
187466565 130833
187466565 134459[/CODE]
n=150000-200000 in progress :showoff:

Cruelty 2005-09-16 17:49

1 Attachment(s)
Attached see primes for k=736320585 for 1<n<250000 (total of 100 primes incl. 2 Sophie Germain).
Continuing sieving and testing.

gribozavr 2005-09-24 20:10

I have finished testing k=187466565 for n=1-200k. I have found some more primes:
[CODE]187466565 160453
187466565 165138
187466565 178879
187466565 187871[/CODE]

Whom do I send the lresults.txt?

Can any of theese primes go into Top-5000? The biggest one is 56564 digits long.

paulunderwood 2005-09-24 20:31

[QUOTE]Can any of theese primes go into Top-5000? The biggest one is 56564 digits long.[/QUOTE]

:no: because they are too small according to:

[url]http://primes.utm.edu/primes/submit.php[/url] which states:

[QUOTE]Currently primes must have 60222 or more digits to make the list[/QUOTE]

In a years time the bar will have been raised to 70k :mad:

grobie 2005-09-28 12:49

Please dont tell me I have been wasting my time :censored: I just noticed the posts from gribozavr and he has already been testing my reserved K-187466565 :rant:

fatphil 2005-10-12 08:10

Back-filling 15k=355424355
 
15k.org lists a gap for 15k=355424355 between n=10000 and 170000.
In that gap you will find:

10982, 14779, 14852, 15331, 15434, 16202, 16303, 16831, 16923, 19875, 21161, 23702, 28127, 29972, 33404

Ongoing...

fatphil 2005-10-14 12:17

[QUOTE=fatphil]15k.org lists a gap for 15k=355424355 between n=10000 and 170000.
In that gap you will find:

10982, 14779, 14852, 15331, 15434, 16202, 16303, 16831, 16923, 19875, 21161, 23702, 28127, 29972, 33404

Ongoing...[/QUOTE]

Beginning to slow down a little, but still progress is good.

39315, 41043, 41592, 51211, 59238, 59772, 60612, 66268

Which, if I'm not mistaken, brings that k to 100 primes. Should I insert a dancing banana here?

It appears to roughly have a density of 7 per n doubling, so another 7-10 in the 70000-170000 range is likely.

fatphil 2005-10-24 11:20

[QUOTE=fatphil]
15k.org lists a gap for 15k=355424355 between n=10000 and 170000.
In that gap you will find:

10982, 14779, 14852, 15331, 15434, 16202, 16303, 16831, 16923, 19875,
21161, 23702, 28127, 29972, 33404, 39315, 41043, 41592, 51211, 59238,
59772, 60612, 66268

Which, if I'm not mistaken, brings that k to 100 primes. Should I insert a dancing banana here?

It appears to roughly have a density of 7 per n doubling, so another 7-10 in the 70000-170000 range is likely.[/QUOTE]

7 more was comparatively easy:

79481, 87840, 91514, 103375, 104433, 106609, 108981

ongoing...

grobie 2005-10-27 18:29

K-55951335
 
I am done with this K untill forum issues are cleared up, or new project starts.

Here are all primes for K-55951335 up to n=100K

n=0 to 10k = 73 primes
55951335 11289
55951335 11578
55951335 11758
55951335 12712
55951335 12844
55951335 13428
55951335 14182
55951335 15692
55951335 16398
55951335 16549
55951335 17906
55951335 31544
55951335 33250
55951335 33904
55951335 43090
55951335 48710
55951335 50294
55951335 50382
55951335 55884
55951335 59910
55951335 72804
55951335 76902
55951335 81033
55951335 92671
55951335 94435
55951335 98733 (99)

fatphil 2005-10-28 09:03

[QUOTE=grobie]I am done with this K untill forum issues are cleared up, or new project starts.
[/QUOTE]

The prime-hunting task, and its worth, should be independent of the website/mailing-list/fora that its participants use to discuss things.

xilman 2005-10-28 09:20

[QUOTE=fatphil]The prime-hunting task, and its worth, should be independent of the website/mailing-list/fora that its participants use to discuss things.[/QUOTE]Well said!

Paul

fatphil 2005-10-30 20:06

3 more for 15k=355424355; now the 15k.org gap looks like this:

10982, 14779, 14852, 15331, 15434, 16202, 16303, 16831, 16923, 19875,
21161, 23702, 28127, 29972, 33404, 39315, 41043, 41592, 51211, 59238,
59772, 60612, 66268, 79481, 87840, 91514, 103375, 104433, 106609, 108981,
129800, 136851, 139247

It should be less than a week before I reach the 170000 where the 15k project started searching for bigger primes. I'm prepared to take on another similar sized gap if there are any other dense candidates deserving of a complete investigation.

lsoule 2005-11-01 00:05

k=8331405 is anther one that may be of interest. It's hundredth
prime occurs at n=45773 (#101 at 47239). It has also yielded 20
primes in the range n=186251-616479

The missing gap is from n=48181-181000

-Larry

fatphil 2005-11-01 08:35

[QUOTE=lsoule]k=8331405 is anther one that may be of interest. It's hundredth
prime occurs at n=45773 (#101 at 47239). It has also yielded 20
primes in the range n=186251-616479

The missing gap is from n=48181-181000

-Larry[/QUOTE]

Thanks Larry!
I shall do that next. I'll start in about 5 days, I guess, and it will take about 2 weeks.

Cheers,
Phil

fatphil 2005-11-08 12:21

[QUOTE=fatphil]Thanks Larry!
I shall do that next. I'll start in about 5 days, I guess, and it will take about 2 weeks.[/QUOTE]

I have seriously overerestimated the speed of my CPU...
Nevertheless, I shall do it as soon as this current batch is done (having a dry patch presently).

fatphil 2005-11-15 11:39

[QUOTE=fatphil]15k=355424355

10982, 14779, 14852, 15331, 15434, 16202, 16303, 16831, 16923, 19875,
21161, 23702, 28127, 29972, 33404, 39315, 41043, 41592, 51211, 59238,
59772, 60612, 66268, 79481, 87840, 91514, 103375, 104433, 106609, 108981,
129800, 136851, 139247[/QUOTE]

that's all folks -- that k is now without n gaps.

The first few small primes have started on my next k too, but I'll wait until I have a whole bunch before starting to post them to keep the noise down.

fatphil 2005-12-01 08:07

I'm nearly half of the way through the hole

k=8331405:
49415
50445
52637
56391
64400
84059
85434
132909

Nice start, shame about the latter dearth.

Phil

Cruelty 2005-12-04 13:10

For k=736320585 I have reached n=410k... so far 99 primes have been discovered, I am still looking for #100 :showoff:

BTW: Maybe we should move this thread to "RPS - forum" :question:

fatphil 2005-12-05 08:57

[QUOTE=Cruelty]For k=736320585 I have reached n=410k... so far 99 primes have been discovered, I am still looking for #100 :showoff:

BTW: Maybe we should move this thread to "RPS - forum" :question:[/QUOTE]


Brave chappy! It'll be there eventually, of course, and it will hopefully be worth the wait. Good luck with that.

Regarding thread location - I have no strong opinion.

On a side note, due to a catastrophic machine failure last week, I'll not be able to do any more small prime back-filling for a while, as I need to move the machine I was using onto sieving. However, it did appear that there weren't any obvious holes in the absolute densest (appearing) candidates.

akruppa 2005-12-05 09:15

Should I move it?

Alex

Cruelty 2005-12-05 12:38

[QUOTE=akruppa]Should I move it?

Alex[/QUOTE] IMO, that would be cool :smile:

ValerieVonck 2005-12-07 08:39

First batch of results for K 3250995
from 10k to 50k:

3250995 12665
3250995 13757
3250995 14730
3250995 18772
3250995 18986
3250995 23930
3250995 26026
3250995 27348
3250995 28051
3250995 31445
3250995 34123
3250995 36262
3250995 38799
3250995 40595
3250995 41002
3250995 42615
3250995 45965
3250995 47757
3250995 48509
3250995 48859

ValerieVonck 2005-12-09 22:23

Tested to k=80k

3250995*2^53311 - 1 is prime! 16055 digits
3250995*2^60917 - 1 is prime! 18345 digits
3250995*2^71729 - 1 is prime! 21600 digits
3250995*2^76722 - 1 is prime! 23103 digits


--
Repasting the other primes with their lenght:

[code]
3250995*2^12665 - 1 is prime! 3820 digits
3250995*2^13757 - 1 is prime! 4148 digits
3250995*2^14730 - 1 is prime! 4441 digits
3250995*2^18772 - 1 is prime! 5658 digits
3250995*2^18986 - 1 is prime! 5722 digits
3250995*2^23930 - 1 is prime! 7211 digits
3250995*2^26026 - 1 is prime! 7842 digits
3250995*2^27348 - 1 is prime! 8240 digits
3250995*2^28051 - 1 is prime! 8451 digits
3250995*2^31445 - 1 is prime! 9473 digits
3250995*2^34123 - 1 is prime! 10279 digits
3250995*2^36262 - 1 is prime! 10923 digits
3250995*2^38799 - 1 is prime! 11687 digits
3250995*2^40595 - 1 is prime! 12227 digits
3250995*2^41002 - 1 is prime! 12350 digits
3250995*2^42615 - 1 is prime! 12835 digits

3250995*2^45965 - 1 is prime! 13844 digits
3250995*2^47757 - 1 is prime! 14383 digits
3250995*2^48509 - 1 is prime! 14610 digits
3250995*2^48859 - 1 is prime! 14715 digits
[/code]

amphoria 2005-12-10 12:56

Primes of 869688105 < n=200000
 
For the record here are all the primes of k=869688105 less than n=200000. All of the larger primes are currently on the Top 5000 list.

[CODE]1, 3, 7, 10, 16, 17, 18, 19, 21, 26, 37, 45, 57, 58, 76, 84, 90,
104, 105, 107, 137, 145, 155, 190, 235, 251, 254, 286, 298, 421,
492, 502, 507, 540 597, 606, 641, 661, 738, 765, 999, 1397, 1487,
1659, 1699, 1815, 2019, 2128, 2326, 2401, 2523, 2736, 2819, 2859,
2898, 2997, 3150, 4084, 4411, 4690, 4842, 6466, 6614, 6632, 8471,
8755, 9067, 9899, 10872, 11862, 12130, 12158, 12264, 12842, 13205,
16257, 18968, 20107, 21783, 24333, 27102, 30777, 31224, 31527,
32235, 32872, 35314, 43604, 48078, 53391, 59191, 64124, 67464,
87768, 88497, 89458, 96851, 115483, 116955, 124675, 131943,
141817, 144768, 153564, 159318, 160002, 165964, 170562[/CODE]

fatphil 2005-12-14 13:06

8331405 back-filled completely
 
15k=8331405's hole contained 9 primes:
49415, 50445, 52637, 56391, 64400, 84059, 85434, 132909, 163192
(I had a few problems with LLR in the middle of that, if anyone would like to have my lresults.txt file, and perhaps double-check the 85434-132909 region, then just ask.)

Can somebody ensure 15k.org is updated?

The full list now stands at 132:

1, 9, 11, 17, 21, 31, 32, 33, 45, 57,
61, 64, 67, 69, 77, 80, 85, 88, 107, 115,
117, 120, 121, 124, 147, 155, 161, 164, 168, 177,
179, 221, 232, 258, 261, 264, 281, 282, 299, 308,
342, 415, 471, 503, 504, 505, 537, 572, 680, 989,
1328, 1565, 1607, 1613, 1841, 1953, 2509, 2692, 2739, 2834,
3627, 3735, 3870, 3960, 4083, 4682, 4788, 5187, 5247, 5623,
5804, 6015, 6020, 6405, 6569, 7052, 7315, 7477, 7489, 8389,
8800, 10407, 10512, 12035, 13015, 14634, 14941, 16339, 16367, 16554,
26533, 28153, 29081, 30222, 32391, 36371, 37323, 39251, 43935, 45052,
45773, 47239, 49415, 50445, 52637,
56391, 64400, 84059, 85434, 132909,
163192, 186251, 198122, 199127, 200363,
205885, 207555, 220532, 222399, 264459,
269433, 274141, 309331, 317435, 359692,
371488, 377268, 383323, 422243, 433420,
585714, 616479

As I'm a machine down for my own project, I'm bowing out of this 15k/RPS back-filling task for the moment, but may rejoin later. Good luck all!

fatphil 2005-12-14 13:12

[QUOTE=fatphil]15k=8331405's hole contained 9 primes:
...
The full list now stands at 132:
[/QUOTE]

I've just noticed that 2995125705 is at 132 too, at roughly the same n level.
Still 10 short of your leader, which is 20 short of my drag race leader.

ValerieVonck 2005-12-15 18:04

[code]
3250995*2^80610 - 1 is prime! 24273 digits
3250995*2^96176 - 1 is prime! 28959 digits
[/code]

Regards,
C.

fatphil 2005-12-16 08:24

Backfilling 15k=25935
 
I noticed that 25935 had a criminally small low hole, so decided to fill it last night:

11476, 12448, 13205, 16282, 19583,
22209, 26443, 28532, 29326, 32689,
34226, 42832, 44325, 46144 already known,
47396 already known, 54956, ... (67364)

No point leaving a hole, so I'll finish this one off too.

ValerieVonck 2005-12-16 20:46

1 more prime to 100k:

[code]
3250995*2^97731-1 is prime! 29427 digits
[/code]

fatphil 2005-12-20 11:42

15k=25935 backfilled completely
 
11476, 12448, 13205, 16282, 19583,
22209, 26443, 28532, 29326, 32689,
34226, 42832, 44325,
(46144 already known, 47396 already known,)
54956, 67599, 69182, 69625, 75563,
81684, 83898, 84676, 91943, 92016,
101560

This brings the total known list to:

1, 3, 4, 9, 10, 11, 12, 16, 19, 21,
23, 25, 29, 32, 33, 35, 44, 48, 64, 80,
82, 99, 100, 101, 128, 132, 141, 155, 170, 201,
213, 339, 570, 573, 623, 698, 721, 811, 826, 964,
1120, 1173, 1185, 1225, 1324, 1329, 1392, 1775, 2056, 2576,
2631, 3045, 3488, 3609, 3803, 4653, 4902, 5064, 5210, 5931,
6013, 6978, 7429, 8163, 8316, 9460, 11476, 12448, 13205, 16282,
19583, 22209, 26443, 28532, 29326, 32689, 34226, 42832, 44325, 46144,
47396, 54956, 67599, 69182, 69625, 75563, 81684, 83898, 84676, 91943,
92016, 101560 117344, 121855, 139225, 152803, 173518, 219995
(220000)

Bugger, that's 98.

Really stopping this time - factorial prime sieving is my next job...
Good luck all.

Kosmaj 2005-12-20 14:51

The [URL=http://www.15k.org/stats.htm]stats page[/URL] updated with small primes found by Phil and Amphoria. Will add those found by Cedric later (cannot locate primes for n<10k for his [I]k[/I]...).

BTW a historic remark on two [I]k[/I]'s included above.
[B]k=25935[/B]
> (46144 already known, 47396 already known,)
These two primes were found in Engelsma (g174) in summer 2000.

[B]k=869688105[/B]
Primes for 27102 <= n <= 48078 were found by Herranen (g78) in November-December 1998.

lsoule 2005-12-23 18:37

Last year I posted the first hundred primes for k=860541825
(The 100th is at n=54696). I have filled in the gaps and taken
this k up to 260k so far. Here are the new primes for a total
of 113 primes so far:

860541825 66286
860541825 67056
860541825 78227
860541825 86092
860541825 95583
860541825 100597
860541825 101104
860541825 102606
860541825 105210
860541825 153367
860541825 170189
860541825 187934
860541825 242559


-Larry

Cruelty 2005-12-23 19:30

1 Attachment(s)
I have started working on k=151515, just for fun :smile: So far 73 primes have been discovered for n<210000, continuing sieving and testing for 210000<n<400000.

grobie 2005-12-29 02:45

k=850612425
 
From Choose your own K, k=850612425 sieved to 312G 10K to 300K, currently at n=244600, Total 100 Primes :down: Will continue to 300k

Primes from n=1 to 10k =77
850612425 10649
850612425 11025
850612425 12050
850612425 12636
850612425 12654
850612425 13294
850612425 23950
850612425 25304
850612425 35537
850612425 46316
850612425 48793
850612425 64345
850612425 78208
850612425 91844
850612425 98819
850612425 107606
850612425 135696
850612425 143231
850612425 153594
850612425 167265
850612425 179716
850612425 219429
850612425 239205 (100th Prime)

ValerieVonck 2005-12-30 19:03

k=234686595
 
From choose your own K

234686595*2^11442 - 1 is prime! 3453 digits
234686595*2^18824 - 1 is prime! 5675 digits
234686595*2^23205 - 1 is prime! 6994 digits
234686595*2^26353 - 1 is prime! 7942 digits
234686595*2^27268 - 1 is prime! 8217 digits
234686595*2^27600 - 1 is prime! 8317 digits
234686595*2^27607 - 1 is prime! 8319 digits
234686595*2^29745 - 1 is prime! 8963 digits
234686595*2^32882 - 1 is prime! 9907 digits
234686595*2^33072 - 1 is prime! 9965 digits

Makes 84 primes! Up to ?? :showoff:

ValerieVonck 2005-12-31 11:12

k=234686595
 
234686595*2^35503 - 1 is prime! 10696 digits
234686595*2^36492 - 1 is prime! 10994 digits
234686595*2^36752 - 1 is prime! 11072 digits
234686595*2^37128 - 1 is prime! 11186 digits
234686595*2^37376 - 1 is prime! 11260 digits
234686595*2^37694 - 1 is prime! 11356 digits
234686595*2^39137 - 1 is prime! 11790 digits
234686595*2^43606 - 1 is prime! 13136 digits
234686595*2^48861 - 1 is prime! 14717 digits
234686595*2^49489 - 1 is prime! 14907 digits

Makes 94 primes!

ValerieVonck 2006-01-01 20:35

234686595*2^50913 - 1 is prime! 15335 digits
234686595*2^62127 - 1 is prime! 18711 digits

Makes 96

grobie 2006-01-03 00:31

From choose you own
 
k=1222853775

Primes from n=1 to 10k = 81
1222853775 12582
1222853775 15111
1222853775 15562
1222853775 17039
1222853775 20909
1222853775 25721
1222853775 27435
1222853775 29005
1222853775 29499
1222853775 29511
1222853775 30871
1222853775 32373
1222853775 32798
1222853775 36441
1222853775 37700
1222853775 45789
1222853775 46062
1222853775 48302
1222853775 52094 (100th Prime) :banana:
1222853775 53967
1222853775 54089
1222853775 55766

grobie 2006-01-04 10:53

[QUOTE=grobie]k=1222853775

Primes from n=1 to 10k = 81
1222853775 12582
1222853775 15111
1222853775 15562
1222853775 17039
1222853775 20909
1222853775 25721
1222853775 27435
1222853775 29005
1222853775 29499
1222853775 29511
1222853775 30871
1222853775 32373
1222853775 32798
1222853775 36441
1222853775 37700
1222853775 45789
1222853775 46062
1222853775 48302
1222853775 52094 (100th Prime) :banana:
1222853775 53967
1222853775 54089
1222853775 55766[/QUOTE]
Finished to 100k, this makes 114 Primes:smile:

1222853775 59546
1222853775 63546
1222853775 71758
1222853775 73031
1222853775 73453
1222853775 76219
1222853775 81370
1222853775 86500
1222853775 86716
1222853775 94574
1222853775 99938

ValerieVonck 2006-01-06 23:15

2 more:

234686595*2^90940 - 1 is prime! 27385 digits
234686595*2^92990 - 1 is prime! 28002 digits

Makes: 98 primes !

Kosmaj 2006-01-07 03:56

Grobie
 
Your [I]k[/I] looks very promissing since the 100th prime occurs early. If you can, keep on testing it to 250 or 300k.

grobie 2006-01-07 10:48

[QUOTE=Kosmaj]Your [I]k[/I] looks very promissing since the 100th prime occurs early. If you can, keep on testing it to 250 or 300k.[/QUOTE]
Yep! As a min to 300k but plan so far to go beyond that. My other k I will drop at 300 k, testing is at 273k now with only 100 primes so far, I just might just drop that one early, what do you think.

grobie 2006-01-11 10:59

Choose your own k:
k=1222853775
This makes 119 primes

1222853775 100189
1222853775 103325
1222853775 105875
1222853775 111050
1222853775 154362

Kosmaj 2006-01-11 11:48

Grobie
 
Cool, IMO it was a good decision to concentrate on this [I]k[/I]. Only the gap between the last two primes is a little bit too large. But let's hope there will be many primes from now on. Just keep on going! :cool:

grobie 2006-01-14 11:55

Choose your own k:
k=1222853775
This makes 122 primes

1222853775 164775
1222853775 169421
1222853775 171257

ValerieVonck 2006-01-15 18:08

Choose your own K:

234686595*2^98272 - 1 is prime! 29592 digits
234686595*2^111766 - 1 is prime! 33654 digits

Makes 100 primes!!

ValerieVonck 2006-01-16 19:35

Choose your own K:

360949875*2^11382-1 3435 digits
360949875*2^12646-1 3816 digits
360949875*2^14164-1 4273 digits
360949875*2^14856-1 4481 digits
360949875*2^16207-1 4888 digits
360949875*2^17228-1 5195 digits
360949875*2^18825-1 5676 digits
360949875*2^19113-1 5763 digits
360949875*2^32748-1 9867 digits
360949875*2^37252-1 11223 digits

Makes 90 primes!!!

lsoule 2006-01-18 22:49

Here are the first 106 primes for k=1952775825. This is one of the k's
in the first RPS drive

1952775825 4
1952775825 5
1952775825 16
1952775825 19
1952775825 23
1952775825 28
1952775825 36
1952775825 47
1952775825 55
1952775825 62
1952775825 64
1952775825 75
1952775825 82
1952775825 90
1952775825 96
1952775825 101
1952775825 111
1952775825 124
1952775825 130
1952775825 132
1952775825 144
1952775825 163
1952775825 169
1952775825 249
1952775825 251
1952775825 254
1952775825 279
1952775825 292
1952775825 296
1952775825 298
1952775825 309
1952775825 318
1952775825 325
1952775825 348
1952775825 364
1952775825 383
1952775825 391
1952775825 396
1952775825 420
1952775825 438
1952775825 444
1952775825 447
1952775825 457
1952775825 491
1952775825 532
1952775825 558
1952775825 560
1952775825 620
1952775825 691
1952775825 850
1952775825 899
1952775825 980
1952775825 1053
1952775825 1058
1952775825 1123
1952775825 1159
1952775825 1254
1952775825 1441
1952775825 1580
1952775825 1927
1952775825 2044
1952775825 2164
1952775825 2228
1952775825 2315
1952775825 2396
1952775825 2449
1952775825 2565
1952775825 3664
1952775825 4147
1952775825 4408
1952775825 4597
1952775825 4765
1952775825 4895
1952775825 4909
1952775825 5191
1952775825 5712
1952775825 6665
1952775825 6740
1952775825 7390
1952775825 8602
1952775825 11123
1952775825 11329
1952775825 12554
1952775825 15120
1952775825 16001
1952775825 16952
1952775825 19804
1952775825 21598
1952775825 22360
1952775825 22692
1952775825 24144
1952775825 27675
1952775825 28058
1952775825 28066
1952775825 29132
1952775825 33297
1952775825 35458
1952775825 44266
1952775825 46850
1952775825 48607
1952775825 55149
1952775825 73821
1952775825 81029
1952775825 83559
1952775825 90765
1952775825 100239

Tested up to n=117419

ValerieVonck 2006-01-21 11:53

360949875*2^46142 - 1 is prime! 13899 digits
360949875*2^48976 - 1 is prime! 14752 digits
360949875*2^60759 - 1 is prime! 18299 digits

Makes 93 primes!

grobie 2006-01-25 11:06

Choose your own k:
k=1222853775
This makes 124 primes < 200k

1222853775 184373
1222853775 184993

progress: box#1 testing n=o to 250k currently at 197277 with 124 primes

box#2 testing n=250 to 300k currently at 270553 with 2 primes

Total 126 Primes

ValerieVonck 2006-01-26 17:48

360949875*2^69027 - 1 is prime! 20788 digits
360949875*2^70726 - 1 is prime! 21300 digits
360949875*2^79219 - 1 is prime! 23856 digits

Makes 96 primes! :showoff:

ValerieVonck 2006-02-01 17:29

360949875*2^107774 - 1 is prime! 32452 digits
360949875*2^111307 - 1 is prime! 33516 digits

Makes 98 primes!

amphoria 2006-02-02 20:30

Primes of k=5169615 < n=210000
 
All the primes of k=5169615 less than n=210000. This k is interesting in that primes are relatively sparse between n=10k and n=100k, but there are quite a few between n=100k and n=200k.

[CODE]5169615 1
5169615 5
5169615 9
5169615 14
5169615 21
5169615 24
5169615 26
5169615 27
5169615 32
5169615 41
5169615 48
5169615 51
5169615 55
5169615 56
5169615 59
5169615 65
5169615 68
5169615 85
5169615 97
5169615 99
5169615 127
5169615 149
5169615 174
5169615 199
5169615 207
5169615 270
5169615 275
5169615 336
5169615 346
5169615 351
5169615 420
5169615 525
5169615 526
5169615 537
5169615 564
5169615 598
5169615 627
5169615 631
5169615 659
5169615 701
5169615 822
5169615 900
5169615 982
5169615 1182
5169615 1289
5169615 1398
5169615 1417
5169615 1466
5169615 1478
5169615 1522
5169615 1776
5169615 2033
5169615 2108
5169615 2144
5169615 2435
5169615 2511
5169615 3471
5169615 3649
5169615 3705
5169615 3786
5169615 3910
5169615 4181
5169615 4618
5169615 5225
5169615 5281
5169615 5285
5169615 5451
5169615 6199
5169615 7112
5169615 7163
5169615 8026
5169615 8677
5169615 11093
5169615 12178
5169615 12582
5169615 15567
5169615 18234
5169615 19368
5169615 24761
5169615 31441
5169615 34229
5169615 39920
5169615 49932
5169615 62435
5169615 86969
5169615 109368
5169615 114065
5169615 121166
5169615 122409
5169615 122865
5169615 131241
5169615 134948
5169615 138531
5169615 146297
5169615 146505
5169615 154275
5169615 158790
5169615 158802
5169615 175677
5169615 183408
5169615 186027
5169615 186357
5169615 199712
5169615 207884
[/CODE]

Kosmaj 2006-02-03 21:40

This one is not so small, but it was not enough for Top-5000.

445419975*2^203536-1 (61280 digits)

I found it back in October but I think I never told anybody about it :smile:

grobie 2006-02-06 11:09

k=1222853775
 
Choose your own k:
k=1222853775
This makes 129 primes

1222853775 210992

progress: box#1 testing n=o to 250k currently at 231177 with 126 primes

box#2 testing n=250 to 300k currently at 293245 with 3 primes

Total 129 Primes

amphoria 2006-02-09 18:35

k=317372055
 
From choose your own k:

317372055 53955
317372055 62185
317372055 63635
317372055 84815

This makes 100 primes for this k. The other 96 for n < 50k were found by Larry.

ValerieVonck 2006-02-12 15:58

k = 360949875
 
360949875*2^114960 - 1 is prime! 34615 digits

Makes 99 primes!

ValerieVonck 2006-02-12 15:59

k = 234686595
 
234686595*2^119958 - 1 is prime! 36120 digits
234686595*2^123788 - 1 is prime! 37273 digits

Makes 102 primes!

ValerieVonck 2006-02-19 10:47

k= 360949875
 
360949875*2^132482 - 1 is prime! 39890 digits

Makes 100 primes!

amphoria 2006-03-01 19:41

k=317372055
 
The remaining primes for this k that did not make it into the Top-5000.

317372055 91950
317372055 94270
317372055 139077
317372055 144290
317372055 149461
317372055 159253
317372055 168581
317372055 181167
317372055 185656
317372055 191704

That makes 110 primes less than 200k, but only two found between 200k and 300k.

ValerieVonck 2006-03-06 17:44

k=234686595
 
234686595*2^143007-1 is primel 43058 digits

Makes 103 primes!

ValerieVonck 2006-03-18 10:58

k= 2028893625
 
2028893625*2^50419-1 is prime! 15187 digits
2028893625*2^53384-1 is prime! 16080 digits
2028893625*2^54248-1 is prime! 16340 digits
2028893625*2^57544-1 is prime! 17332 digits

Makes 102 primes

ValerieVonck 2006-04-05 16:29

2028893625*2^66796 - 1 is prime! 20117 digits
2028893625*2^85724 - 1 is prime! 25815 digits

Makes 104 primes!

ValerieVonck 2006-04-08 13:13

2028893625*2^104208 - 1 is prime! 31380 digits
2028893625*2^109300 - 1 is prime! 32912 digits

Makes 106 primes!

ValerieVonck 2006-04-16 09:49

2028893625*2^128161 - 1 is prime! 38590 digits
2028893625*2^128776 - 1 is prime! 38775 digits

Makes 108 primes.

Cruelty 2006-04-19 11:34

1 Attachment(s)
Attached is a list of primes for k=12345 and n<240000 - none reportable to TOP-5000 list yet.
I will continue testing this "k".

Cruelty 2006-04-19 11:35

1 Attachment(s)
Attached is a list of primes for k=617 and n<240000 - none reportable to TOP-5000 list yet.
I will continue testing this "k".

Cruelty 2006-04-24 17:33

I have reached n=500000 for k=736320585. So far I have found 101 primes for this "k"... I'm still on it :flex:

Cruelty 2006-07-05 08:06

Two milestones to report:
k=617 tested till n=600000 (it's not a part of RPS)
k=12345 tested till n=400000

I'm still working on both "k" :smile:

Cruelty 2006-07-12 20:58

1 Attachment(s)
Attached is a list of primes for k=1515 and n<240000 - none reportable to TOP-5000 list yet.
I will continue testing this "k".

Cruelty 2006-08-25 17:38

k=151515 tested till n=600000 - no primes to report in range 400000<n<600000.
I am still testing this "k" :smile:

ValerieVonck 2007-01-22 13:36

k=686701125
 
686701125*2^59037 - 1 is prime! 17781 digits
686701125*2^61564 - 1 is prime! 18542 digits
686701125*2^61743 - 1 is prime! 18596 digits
686701125*2^71904 - 1 is prime! 21655 digits

ValerieVonck 2007-01-24 14:28

[code]
686701125*2^77984 - 1 is prime! 23485 digits
686701125*2^82487 - 1 is prime! 24840 digits
[/code]

ValerieVonck 2007-01-31 21:21

k=686701125
 
[CODE] 686701125*2^85355 -1 is prime! 25704 digits
686701125*2^86208 -1 is prime! 25961 digits
686701125*2^92474 -1 is prime! 27847 digits
686701125*2^101321 -1 is prime! 30510 digits[/CODE]

kar_bon 2007-02-21 06:07

475977645 199782 is prime (60150 digits)

Thomas11 2007-03-02 11:03

new best k found...
 
For [B]k=37850187375[/B] (Nash weight: 7261) the 100th prime appeared at [B]n=13719[/B] :w00t:

Here is the list of n which yield primes up to n=24000:
[CODE]2, 5, 13, 16, 19, 20, 41, 56, 57, 64, 66, 74, 90, 97, 100, 107, 130,
137, 145, 147, 149, 171, 172, 178, 208, 241, 258, 301, 302, 318, 330,
331, 386, 439, 460, 462, 526, 529, 556, 558, 563, 625, 626, 628, 666,
699, 797, 804, 890, 907, 928, 968, 1050, 1117, 1247, 1304, 1453, 1584,
1782, 1788, 2115, 2193, 2239, 2371, 2439, 2533, 2789, 2827, 2984, 3044,
3382, 3568, 3633, 3884, 3900, 3909, 4406, 4426, 5833, 6241, 6283, 6325,
6580, 6596, 6714, 7621, 7727, 7968, 8323, 8817, 9002, 9258, 9833, 11742,
11868, 12248, 12294, 12754, 13340, 13719, 15527, 15913, 16323, 16554,
19362, 19802, 20013, 22376[/CODE]

kar_bon 2007-03-07 07:30

475977645*2^207784-1 (62558 digits)

nuggetprime 2007-03-13 17:03

k=19217385 tested from 50k to 70k.
There are primes for the following n:
60121
62263
64849
66746 <----- 100th prime

kuratkull 2007-03-19 06:19

k=228461805
 
I decided to sieve and LLR some smaller N's for my K, which is already being sieved and LLR'd from 300k-500k.

228461805*2^102923-1 is prime! (30992 digits)

Templus 2007-03-19 19:08

I am currently working on 2 k's :

11069*2^n-1 : (on other machine) done until 450k
21879*2^n-1 : 28, 232, 244, 292, 448, 2068, 17548, 64288 ; done until 300k


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