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Old 2004-02-27, 07:02   #1
Kosmaj
 
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Nov 2003

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Default 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.
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Old 2004-03-16, 19:46   #2
cyrix
 
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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

Last fiddled with by Kosmaj on 2007-07-27 at 23:46 Reason: n's moved in-line
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Old 2004-03-16, 21:53   #3
cyrix
 
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Oh, a typing error: Actual k=1581823815.
Cyrix
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Old 2004-03-17, 01:31   #4
Kosmaj
 
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Then this is now our "best k" since the 100th prime occured for n=38374. The previous best was k=2995125705, and i(100)=60190.
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Old 2004-03-19, 08:09   #5
BotXXX
 
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I tested the 15k = 968911515 from n=2 to n=50000 and found the following primes. I will not 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
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Old 2004-03-19, 11:59   #6
BotXXX
 
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I also tested the 15k = 475977645 from n=2 to n=50000 and found the following primes. I will not 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

Last fiddled with by BotXXX on 2004-03-19 at 12:00 Reason: typos
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Old 2005-01-06, 18:55   #7
lsoule
 
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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
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Old 2005-01-21, 16:04   #8
lsoule
 
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32508 Posts
Default 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
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Old 2005-03-10, 23:06   #9
lsoule
 
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[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
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Old 2005-03-11, 16:35   #10
masser
 
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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
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Old 2005-03-16, 21:46   #11
lsoule
 
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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
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