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Old 2005-03-16, 22:40   #12
Kosmaj
 
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Nov 2003

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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 here.
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Old 2005-03-16, 23:45   #13
robert44444uk
 
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Jun 2003
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Default 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
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Old 2005-03-16, 23:49   #14
robert44444uk
 
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Default 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
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Old 2005-04-17, 09:06   #15
gribozavr
 
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Default 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
I will continue testing this 15k with n up to 200000.
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Old 2005-04-21, 03:46   #16
VBCurtis
 
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Feb 2005
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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
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Old 2005-04-21, 04:06   #17
lsoule
 
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The top-5000 cutoff is just below n=189,000 now.

-Larry
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Old 2005-04-25, 18:47   #18
gribozavr
 
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Default 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. So, please, give us both a credit for theese primes (write something like gribozavr and yasya):
Code:
187466565 107376
187466565 109098
187466565 111081
187466565 127062
187466565 130833
187466565 134459
n=150000-200000 in progress
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Old 2005-09-16, 17:49   #19
Cruelty
 
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Attached see primes for k=736320585 for 1<n<250000 (total of 100 primes incl. 2 Sophie Germain).
Continuing sieving and testing.
Attached Files
File Type: txt PRIMES_736320585_250k.txt (2.0 KB, 183 views)
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Old 2005-09-24, 20:10   #20
gribozavr
 
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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
Whom do I send the lresults.txt?

Can any of theese primes go into Top-5000? The biggest one is 56564 digits long.
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Old 2005-09-24, 20:31   #21
paulunderwood
 
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Quote:
Can any of theese primes go into Top-5000? The biggest one is 56564 digits long.
because they are too small according to:

http://primes.utm.edu/primes/submit.php which states:

Quote:
Currently primes must have 60222 or more digits to make the list
In a years time the bar will have been raised to 70k
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Old 2005-09-28, 12:49   #22
grobie
 
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Please dont tell me I have been wasting my time I just noticed the posts from gribozavr and he has already been testing my reserved K-187466565
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