mersenneforum.org  

Go Back   mersenneforum.org > Prime Search Projects > Twin Prime Search

Reply
 
Thread Tools
Old 2007-06-23, 22:11   #1
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

27F316 Posts
Default List of most small twins of form k*2^n+/-1

To whom may be interested,

I went through an excercise to find an easy way to get most of the primes of the form k * 2 ^ n +/- 1 with small values of k. What I did was I extracted all of the k's and n's from the RPS site, the Primesearch site, and the Proth search site into Excel spreadsheets. I then used Excel formulas to match up primes for the -1 sites (RPS and Primesearch) to the +1 site (Proth). The largest value of k that I could use was 599 because that is the highest that the Proth search site goes to.

Attached is a Notepad file that shows what I came up with. The first part is sorted by n. The second part by k.

Although the largest twins that I found don't come close to the top 10 or 20 twins, I think it's good to have comprehensive lists like this as 'building blocks' for future searches.

The largest twins that I found from the effort are:
1. 459 * 2 ^ 8529 +/- 1
2. 291 * 2 ^ 1553 +/- 1
3. 177 * 2 ^ 1032 +/- 1

Not too bad considering I could only match up to k=599. Obviously this list is constrainted by the lower limits of how far each k has been searched for BOTH Riesel primes and Proth primes.

If anyone knows of a more comprehensive list of Proth primes (i.e. of the form k * 2^n + 1) where k > 600 like we have at RPS for Rielsel primes, I'll extend this effort to include more k's.



Gary
Attached Files
File Type: txt twin primes match.txt (3.7 KB, 365 views)
gd_barnes is online now   Reply With Quote
Old 2007-06-24, 05:56   #2
Citrix
 
Citrix's Avatar
 
Jun 2003

32·52·7 Posts
Default

Here are twins from k=1 to 10145 (used this limit as LLR is faster for these k's) and corresponding twin n's upto n=250. Would like to extend these further, anyone want to help. I think k=1-300 have been searched enough.

Code:
3 1
3 2
3 6
3 18
9 1
9 3
9 7
9 43
9 63
9 211
15 1
15 2
15 4
15 10
21 1
21 7
27 2
27 4
33 6
33 22
39 3
45 2
45 9
45 14
45 29
45 189
51 1
51 9
57 2
57 8
57 10
63 14
69 1
69 19
75 1
75 3
75 6
75 43
81 5
81 21
81 27
87 2
87 8
93 4
93 10
99 1
99 5
99 11
99 65
105 2
105 5
105 8
105 155
117 4
117 6
117 16
129 3
129 5
129 59
135 1
135 10
135 238
141 1
141 7
141 61
147 44
147 60
165 2
165 3
165 5
165 12
165 39
165 84
177 12
177 48
195 4
195 8
195 14
201 3
201 9
207 2
213 36
213 80
231 1
231 7
243 12
243 18
243 24
255 2
255 41
261 1
261 3
261 9
267 4
267 34
267 40
273 2
273 10
285 1
297 14
309 1
309 143
315 22
315 72
321 1
321 5
327 4
333 54
339 3
339 11
345 4
345 15
345 30
345 40
345 150
357 2
357 10
357 14
363 2
369 13
375 3
375 14
375 26
375 33
381 17
381 21
387 28
387 88
399 11
405 1
405 2
405 46
405 80
411 1
411 19
417 2
417 8
417 62
423 8
429 1
429 9
429 37
435 4
441 1
441 3
441 13
441 181
447 2
447 20
453 48
459 3
459 9
465 6
465 9
471 3
483 2
483 18
483 22
489 5
495 16
495 33
507 2
507 26
513 6
513 12
519 11
519 55
525 1
525 6
525 8
525 26
525 190
531 1
537 6
537 102
549 11
555 9
555 27
561 7
567 2
585 2
585 32
585 57
591 5
597 70
603 10
603 76
609 19
615 1
615 14
621 3
627 6
633 32
639 1
639 13
645 1
645 5
645 7
651 1
657 58
663 24
669 11
675 5
675 9
675 15
675 26
681 31
687 34
699 5
699 125
705 3
705 6
711 17
717 12
723 6
723 16
735 3
735 20
735 21
741 1
741 7
741 11
741 35
747 6
759 17
765 4
765 10
765 12
765 18
765 22
765 25
765 168
777 10
795 3
813 2
813 4
813 58
819 3
819 63
825 2
831 9
843 2
843 20
849 1
849 3
849 45
849 91
855 4
855 10
855 11
861 1
861 25
867 2
867 8
879 17
885 2
885 14
885 17
891 3
897 28
903 4
903 6
915 22
915 25
915 55
915 70
921 15
927 50
933 40
939 1
945 3
945 8
945 12
951 13
957 22
963 2
975 1
975 24
975 37
981 5
993 4
993 8
993 14
999 1
999 13
1005 2
1011 3
1017 12
1023 2
1023 242
1029 3
1029 7
1035 8
1035 14
1041 1
1053 14
1065 1
1065 2
1065 28
1065 56
1071 1
1071 7
1071 25
1089 5
1089 15
1089 131
1095 9
1095 42
1101 37
1107 50
1119 1
1119 13
1125 3
1125 51
1125 58
1125 63
1125 123
1131 15
1137 2
1143 4
1155 1
1155 3
1155 18
1155 31
1179 3
1179 11
1179 23
1179 51
1179 141
1185 25
1191 1
1191 61
1197 2
1197 10
1197 16
1197 52
1197 70
1197 206
1203 104
1209 9
1215 3
1221 3
1233 2
1233 16
1245 5
1251 3
1257 6
1263 6
1269 37
1275 1
1275 2
1275 31
1281 17
1281 23
1287 8
1299 11
1305 5
1305 32
1323 106
1329 1
1329 65
1335 15
1347 12
1353 4
1365 1
1365 4
1365 12
1365 39
1383 176
1389 21
1395 1
1395 3
1395 7
1395 21
1395 43
1401 1
1401 17
1401 37
1407 12
1413 2
1419 3
1419 15
1419 147
1431 23
1437 6
1443 8
1455 16
1455 85
1455 133
1467 2
1467 6
1467 14
1467 92
1479 3
1479 19
1485 1
1485 17
1485 58
1491 5
1491 17
1491 29
1491 47
1497 122
1509 3
1509 21
1509 125
1515 5
1515 105
1527 16
1527 20
1533 2
1539 7
1545 10
1545 34
1545 82
1551 9
1551 33
1575 2
1575 6
1575 13
1575 16
1575 20
1581 5
1587 76
1593 26
1599 9
1605 12
1611 19
1617 10
1617 20
1623 22
1623 52
1623 64
1629 1
1629 7
1629 13
1629 87
1635 11
1641 11
1659 5
1665 1
1665 2
1665 5
1665 25
1677 14
1695 1
1695 2
1695 46
1707 2
1713 4
1719 33
1725 23
1725 26
1731 1
1731 39
1737 2
1737 4
1743 14
1743 28
1755 204
1761 17
1767 50
1779 1
1785 30
1791 1
1791 7
1797 4
1803 2
1809 15
1815 16
1827 2
1827 6
1833 2
1833 16
1863 20
1863 32
1869 7
1869 17
1869 23
1869 47
1875 17
1881 15
1881 169
1887 2
1887 12
1887 62
1893 8
1899 19
1911 1
1911 3
1911 5
1911 41
1923 22
1935 8
1935 12
1935 188
1941 49
1941 175
1947 4
1953 4
1959 1
1959 7
1959 49
1965 1
1965 10
1983 4
1983 124
1989 5
1995 5
1995 6
1995 14
1995 16
1995 21
1995 26
1995 39
2001 1
2001 19
2001 29
2001 53
2013 6
2025 1
2037 6
2055 2
2055 20
2061 9
2061 35
2067 4
2067 12
2067 22
2073 2
2079 1
2079 3
2079 31
2079 81
2079 103
2091 7
2097 2
2097 14
2097 36
2103 6
2109 1
2115 1
2115 14
2115 173
2121 1
2121 163
2127 4
2127 22
2127 50
2133 4
2133 58
2139 5
2151 3
2151 15
2157 2
2157 4
2157 124
2163 16
2163 20
2163 60
2169 1
2175 6
2175 43
2175 111
2181 29
2181 33
2181 131
2187 6
2187 30
2187 36
2205 2
2205 4
2205 7
2205 19
2205 40
2205 110
2211 1
2211 7
2211 19
2211 49
2217 12
2229 5
2241 1
2241 5
2241 13
2253 2
2253 20
2259 1
2265 3
2265 81
2271 5
2271 9
2271 45
2277 10
2277 178
2283 4
2289 3
2289 9
2289 11
2295 14
2295 47
2313 14
2319 1
2319 7
2319 61
2325 1
2325 4
2331 21
2343 30
2349 5
2355 2
2355 12
2355 32
2361 1
2361 25
2373 36
2385 3
2385 6
2385 22
2397 6
2403 4
2403 52
2409 11
2415 9
2415 10
2415 54
2433 32
2445 15
2457 46
2457 74
2463 16
2469 3
2469 7
2469 67
2487 6
2487 12
2487 18
2493 184
2499 3
2499 17
2499 21
2505 1
2511 1
2517 2
2517 62
2523 2
2523 20
2529 3
2535 2
2535 53
2547 10
2547 14
2553 4
2565 126
2571 21
2571 231
2577 4
2577 76
2583 2
2583 6
2595 4
2595 7
2595 46
2601 3
2601 5
2607 2
2607 6
2607 20
2613 24
2625 2
2625 21
2625 31
2631 7
2649 3
2655 7
2655 49
2661 19
2673 8
2673 116
2679 49
2685 9
2685 54
2691 5
2691 9
2697 10
2697 12
2697 28
2697 78
2703 14
2703 16
2709 1
2709 19
2715 2
2715 13
2721 1
2721 105
2733 48
2739 1
2739 9
2739 13
2745 7
2751 1
2757 40
2769 5
2769 33
2775 5
2781 7
2787 14
2793 2
2805 15
2805 27
2811 15
2817 6
2829 1
2829 5
2835 63
2847 172
2859 17
2865 30
2871 1
2889 7
2895 5
2895 8
2895 11
2895 51
2913 26
2919 35
2925 1
2925 2
2925 13
2925 37
2925 67
2937 44
2943 20
2955 5
2955 7
2961 3
2961 7
2961 17
2967 10
2967 16
2979 3
2985 2
2985 14
2985 66
2997 10
2997 50
3003 6
3015 16
3027 2
3027 18
3039 11
3045 1
3045 22
3057 18
3057 52
3063 2
3063 44
3069 11
3075 4
3081 7
3081 73
3087 4
3087 6
3087 112
3093 10
3093 38
3099 1
3105 8
3105 134
3111 27
3111 41
3117 6
3117 132
3123 34
3129 3
3129 15
3135 1
3135 2
3135 44
3135 74
3153 2
3153 14
3153 30
3165 5
3165 10
3165 20
3183 12
3189 9
3195 17
3213 16
3213 56
3219 7
3219 29
3225 1
3225 3
3225 13
3231 3
3231 5
3231 15
3243 12
3243 16
3249 5
3249 29
3249 41
3255 11
3255 32
3273 24
3273 60
3285 1
3285 7
3285 57
3303 118
3315 21
3315 27
3321 89
3327 4
3339 3
3339 13
3339 37
3339 93
3345 1
3351 1
3351 9
3363 8
3369 3
3369 9
3369 15
3375 10
3375 26
3381 1
3381 5
3399 11
3399 15
3399 23
3399 33
3399 57
3405 3
3405 5
3405 8
3405 27
3405 227
3417 16
3423 2
3429 61
3435 1
3435 3
3435 33
3441 3
3441 15
3447 20
3453 42
3465 4
3465 5
3465 10
3465 14
3465 24
3465 35
3465 80
3471 7
3477 4
3477 12
3477 24
3477 52
3483 2
3489 35
3495 6
3495 28
3507 10
3507 46
3513 4
3513 70
3519 13
3525 9
3525 44
3537 10
3549 19
3555 5
3555 16
3555 137
3579 15
3591 7
3591 63
3591 77
3597 2
3603 34
3615 212
3627 14
3633 14
3633 54
3639 41
3651 3
3651 111
3657 2
3663 22
3663 78
3669 25
3675 1
3675 3
3675 12
3675 29
3675 36
3681 79
3693 20
3699 23
3705 15
3717 2
3717 4
3717 16
3717 164
3729 1
3735 3
3741 153
3747 94
3765 8
3765 10
3765 35
3771 7
3777 20
3783 36
3789 9
3795 1
3795 5
3795 52
3801 5
3813 30
3819 5
3825 5
3825 11
3837 8
3849 7
3855 3
3855 33
3861 5
3867 38
3879 1
3879 11
3879 29
3879 35
3885 3
3885 6
3885 7
3885 8
3885 20
3909 9
3915 3
3915 123
3915 147
3927 10
3933 2
3933 4
3933 10
3933 14
3939 1
3939 3
3957 4
3957 120
3963 10
3963 38
3969 11
3975 1
3975 4
3981 3
3981 13
3981 61
3993 2
3993 12
4005 1
4005 8
4011 11
4011 27
4011 51
4017 2
4017 16
4029 23
4029 29
4035 2
4035 5
4035 8
4035 23
4035 60
4035 62
4047 2
4059 7
4059 25
4059 31
4059 241
4065 12
4077 12
4089 35
4089 83
4095 4
4095 18
4095 125
4107 100
4113 2
4119 9
4125 27
4125 87
4131 49
4137 82
4143 140
4155 56
4155 174
4161 3
4161 75
4167 6
4173 2
4173 10
4173 32
4185 14
4191 7
4209 9
4215 1
4215 106
4221 3
4221 11
4221 35
4239 5
4245 2
4245 198
4257 2
4257 4
4263 4
4269 1
4275 10
4275 39
4281 5
4287 180
4299 1
4299 125
4305 4
4305 16
4311 11
4311 77
4323 2
4323 6
4323 8
4323 12
4323 36
4329 15
4347 2
4347 6
4347 8
4353 10
4359 81
4365 51
4383 14
4389 17
4395 2
4407 20
4419 1
4431 1
4431 3
4437 2
4449 3
4449 29
4449 39
4449 53
4455 6
4461 13
4467 4
4467 124
4467 128
4473 26
4473 76
4473 92
4485 1
4485 28
4497 2
4497 68
4497 152
4509 7
4515 2
4515 5
4515 19
4521 1
4521 7
4521 29
4527 24
4527 58
4533 2
4533 8
4545 13
4557 6
4563 2
4569 27
4575 8
4575 9
4575 104
4599 3
4599 19
4605 4
4605 10
4611 15
4623 6
4635 2
4635 4
4641 1
4647 8
4671 1
4677 10
4695 7
4695 10
4713 132
4719 1
4719 5
4725 35
4731 1
4731 83
4743 6
4749 3
4749 5
4749 11
4749 35
4749 41
4755 4
4761 11
4761 17
4767 42
4773 4
4773 64
4785 2
4785 47
4791 3
4791 15
4803 2
4803 10
4803 32
4809 5
4815 1
4815 5
4821 3
4821 13
4821 49
4827 6
4833 6
4839 1
4839 3
4845 2
4845 7
4851 9
4857 2
4857 4
4857 8
4857 22
4857 32
4857 58
4863 22
4869 141
4887 4
4893 6
4899 7
4905 3
4905 19
4929 1
4929 79
4935 7
4935 12
4935 14
4935 16
4935 17
4947 4
4947 28
4953 14
4965 1
4965 37
4977 4
4977 8
4995 6
5001 5
5001 11
5013 4
5013 10
5019 1
5019 3
5019 19
5019 45
5025 20
5025 125
5031 19
5037 2
5043 8
5043 14
5049 7
5055 10
5055 40
5055 68
5061 23
5073 12
5079 5
5091 7
5097 4
5103 4
5115 9
5115 30
5115 58
5127 2
5127 6
5127 12
5133 6
5139 5
5139 17
5145 39
5145 48
5151 1
5151 41
5163 6
5163 116
5187 2
5187 20
5193 2
5193 44
5205 47
5229 1
5229 77
5241 15
5247 6
5253 2
5259 3
5259 69
5259 153
5265 1
5265 2
5271 41
5277 10
5283 168
5295 14
5295 50
5301 3
5325 4
5331 11
5343 6
5343 28
5343 36
5349 5
5355 1
5355 3
5373 2
5379 9
5385 9
5385 39
5385 40
5385 57
5397 2
5397 4
5397 14
5403 2
5403 16
5415 3
5415 6
5433 4
5433 14
5439 5
5445 1
5445 4
5445 8
5451 3
5451 7
5451 27
5451 33
5469 1
5469 13
5475 13
5475 25
5475 103
5481 5
5481 11
5481 185
5493 34
5499 11
5505 5
5505 57
5505 80
5511 3
5511 21
5523 2
5523 6
5523 32
5529 1
5529 205
5535 1
5535 3
5535 7
5535 48
5535 78
5541 9
5547 6
5553 16
5559 1
5559 5
5559 11
5565 7
5565 13
5565 14
5565 119
5571 29
5577 6
5583 8
5589 99
5595 4
5595 30
5607 14
5607 24
5625 5
5625 69
5643 2
5643 38
5649 9
5649 23
5655 2
5655 19
5655 44
5661 51
5679 9
5679 13
5685 2
5685 8
5697 4
5697 76
5709 15
5715 2
5715 14
5715 149
5727 14
5727 26
5733 16
5745 1
5745 10
5757 2
5757 12
5769 5
5775 1
5775 4
5775 7
5775 19
5781 7
5787 12
5787 48
5793 84
5799 5
5805 3
5805 18
5805 84
5823 2
5835 3
5835 9
5835 27
5835 45
5835 129
5847 22
5859 1
5859 27
5859 31
5859 81
5859 215
5865 7
5865 26
5865 50
5871 25
5889 1
5901 5
5907 2
5919 3
5925 15
5925 35
5943 4
5943 10
5949 5
5949 11
5955 7
5955 16
5961 117
5967 8
5985 1
6015 3
6015 13
6015 36
6021 1
6021 25
6027 2
6027 12
6027 42
6033 20
6033 32
6033 38
6039 3
6039 39
6045 2
6045 8
6051 3
6057 22
6063 20
6063 40
6063 130
6069 9
6081 1
6081 3
6087 6
6093 2
6093 12
6099 19
6105 2
6105 10
6105 16
6105 17
6105 46
6105 80
6117 56
6123 24
6129 3
6129 135
6147 50
6159 7
6165 4
6165 34
6171 3
6177 20
6183 4
6183 82
6189 1
6195 20
6195 26
6195 57
6195 92
6201 19
6207 54
6225 7
6231 7
6231 79
6237 46
6249 3
6249 13
6249 37
6249 63
6273 8
6273 10
6273 16
6279 5
6279 33
6285 5
6285 56
6297 14
6321 41
6327 2
6327 80
6333 24
6333 54
6345 20
6351 99
6369 5
6375 4
6375 13
6375 18
6381 9
6393 18
6405 3
6411 1
6417 34
6435 3
6435 36
6441 17
6459 1
6465 3
6465 14
6471 3
6477 22
6483 2
6489 9
6501 1
6501 45
6501 175
6531 5
6531 13
6549 5
6549 9
6549 15
6549 59
6555 11
6555 21
6555 162
6555 221
6561 33
6561 43
6567 116
6573 12
6573 22
6579 7
6585 4
6585 52
6591 5
6609 1
6615 217
6627 4
6627 12
6627 18
6639 95
6645 4
6645 6
6645 9
6645 37
6669 1
6669 21
6675 2
6675 15
6675 51
6687 6
6693 80
6699 1
6699 3
6705 5
6705 7
6705 10
6705 25
6711 19
6717 6
6717 12
6723 2
6729 61
6735 34
6765 2
6765 6
6765 30
6771 19
6777 2
6783 6
6783 12
6783 60
6795 19
6795 45
6807 6
6807 8
6825 4
6825 30
6825 42
6825 60
6831 23
6831 29
6837 10
6843 44
6855 1
6861 1
6879 1
6885 2
6891 5
6897 10
6897 108
6903 142
6915 1
6915 31
6915 37
6927 14
6927 56
6939 1
6945 4
6945 7
6951 1
6951 9
6957 20
6963 6
6963 12
6963 16
6969 5
6975 6
6975 11
6975 12
6975 59
6975 74
6981 27
6981 205
6987 28
6999 1
6999 41
7005 1
7005 3
7023 24
7023 64
7029 23
7029 35
7029 71
7035 8
7035 48
7035 122
7041 1
7041 7
7059 9
7059 11
7059 23
7065 4
7065 6
7065 39
7065 66
7071 25
7077 2
7083 4
7083 28
7089 3
7089 7
7095 17
7095 30
7101 3
7101 5
7107 6
7119 7
7125 1
7125 8
7125 20
7137 2
7137 6
7143 2
7143 6
7143 24
7143 30
7149 3
7155 2
7155 5
7155 8
7155 13
7161 1
7161 15
7161 57
7167 8
7179 9
7179 11
7179 15
7179 39
7179 45
7185 8
7191 3
7191 9
7197 4
7203 10
7203 28
7203 32
7215 34
7221 185
7245 5
7245 12
7245 14
7245 17
7245 69
7245 102
7245 107
7257 10
7257 88
7263 8
7269 3
7275 1
7281 1
7281 17
7281 19
7293 4
7299 3
7305 3
7305 119
7305 128
7311 11
7317 12
7329 5
7329 61
7335 7
7335 11
7335 35
7341 15
7341 135
7347 2
7347 6
7347 8
7347 108
7353 8
7359 9
7365 4
7377 94
7383 10
7383 172
7389 11
7395 20
7401 3
7401 25
7419 7
7425 4
7443 4
7449 17
7455 60
7455 74
7473 6
7479 29
7485 12
7485 40
7485 57
7491 5
7503 2
7503 4
7515 17
7515 33
7521 3
7533 8
7533 52
7539 35
7539 75
7545 19
7545 31
7545 103
7551 37
7569 1
7569 159
7575 11
7575 25
7581 3
7593 16
7611 3
7617 2
7623 2
7623 30
7635 1
7635 6
7647 6
7653 6
7665 1
7665 10
7665 40
7671 5
7671 7
7671 35
7677 6
7695 3
7695 9
7695 93
7713 2
7719 33
7725 111
7731 5
7737 96
7737 166
7749 7
7749 9
7755 10
7755 17
7755 47
7767 26
7791 1
7797 10
7809 21
7809 29
7809 47
7821 1
7821 7
7845 6
7845 30
7851 5
7851 99
7857 8
7863 6
7863 22
7863 60
7869 1
7875 11
7881 103
7887 114
7917 6
7923 14
7929 61
7935 32
7947 222
7953 4
7977 12
7989 21
7995 5
7995 8
7995 47
8001 5
8001 15
8007 2
8007 4
8013 10
8019 3
8025 5
8031 1
8037 16
8037 76
8055 43
8061 77
8067 14
8067 26
8079 53
8085 44
8085 61
8091 25
8097 6
8097 46
8097 52
8103 2
8103 12
8109 11
8109 21
8115 1
8115 3
8115 10
8115 189
8121 53
8121 139
8127 18
8127 26
8133 2
8133 14
8133 34
8145 45
8157 24
8163 74
8175 8
8175 13
8181 1
8181 3
8193 6
8199 7
8205 7
8205 16
8205 26
8211 7
8211 35
8223 18
8223 28
8235 2
8235 5
8235 12
8235 27
8241 3
8241 21
8241 31
8253 4
8265 97
8265 199
8283 4
8289 5
8289 7
8289 13
8289 55
8295 2
8295 3
8319 21
8325 1
8325 10
8325 12
8325 70
8337 2
8337 192
8355 30
8367 6
8373 8
8373 10
8385 28
8397 2
8397 14
8409 3
8415 1
8415 11
8415 13
8415 23
8415 29
8415 38
8421 13
8421 15
8421 107
8427 52
8433 6
8445 5
8445 23
8451 1
8457 2
8457 56
8469 17
8475 4
8493 6
8499 5
8499 11
8499 25
8505 7
8505 51
8511 5
8511 49
8511 185
8517 6
8523 12
8535 3
8535 6
8535 39
8541 5
8541 47
8547 4
8547 8
8553 2
8559 43
8565 2
8565 15
8565 135
8571 45
8583 34
8589 3
8589 7
8595 1
8613 6
8619 37
8625 2
8625 44
8631 7
8631 9
8631 19
8649 3
8649 21
8655 6
8673 14
8673 18
8673 62
8679 83
8685 22
8691 11
8691 27
8697 6
8709 1
8709 5
8715 5
8715 6
8715 30
8721 127
8727 12
8727 60
8739 125
8745 1
8745 9
8745 12
8757 74
8763 2
8775 3
8775 51
8781 11
8787 16
8793 32
8799 1
8805 23
8811 3
8823 26
8829 1
8835 10
8841 1
8841 5
8841 9
8841 19
8841 29
8841 99
8847 14
8853 16
8859 5
8859 69
8865 3
8865 8
8877 2
8877 116
8883 2
8883 68
8895 1
8901 5
8907 6
8913 4
8919 1
8919 7
8919 31
8925 6
8949 5
8955 1
8955 21
8955 24
8961 1
8961 5
8973 4
8973 10
8979 1
8985 3
9003 2
9009 17
9021 1
9021 3
9021 9
9021 37
9027 2
9033 20
9033 50
9039 199
9051 13
9051 217
9057 20
9063 4
9063 6
9063 166
9069 23
9081 3
9087 16
9087 22
9087 34
9087 62
9093 16
9099 5
9105 4
9105 6
9105 13
9105 19
9105 60
9117 2
9117 8
9117 20
9123 4
9135 18
9135 24
9135 30
9141 25
9141 67
9159 15
9159 21
9165 13
9165 16
9189 51
9195 2
9195 12
9201 3
9207 82
9219 13
9225 2
9225 5
9225 11
9225 17
9225 101
9225 214
9231 3
9231 43
9237 24
9243 8
9249 15
9249 51
9255 2
9255 56
9261 1
9273 96
9279 9
9285 9
9285 77
9285 78
9291 15
9297 10
9297 20
9303 24
9327 2
9327 6
9345 3
9345 4
9345 55
9345 93
9357 4
9375 16
9381 5
9387 2
9387 20
9393 2
9405 27
9405 95
9411 17
9417 6
9423 2
9423 4
9435 4
9435 10
9435 76
9441 15
9453 2
9459 1
9459 37
9465 8
9465 35
9483 12
9483 34
9483 36
9489 5
9489 39
9495 78
9519 65
9525 6
9549 17
9555 5
9555 30
9555 91
9567 4
9585 6
9585 21
9591 1
9591 23
9591 47
9603 8
9609 3
9609 13
9615 2
9615 14
9615 17
9621 5
9621 17
9645 5
9651 67
9663 2
9681 11
9687 2
9687 10
9693 28
9693 42
9699 15
9699 99
9705 36
9711 1
9711 3
9717 10
9717 16
9723 22
9735 1
9741 5
9741 29
9747 48
9753 36
9753 196
9759 23
9765 21
9771 1
9789 9
9801 7
9801 35
9807 2
9807 24
9825 5
9825 6
9837 6
9843 2
9843 20
9849 1
9849 11
9849 121
9861 3
9861 33
9867 108
9873 32
9885 7
9885 32
9897 14
9903 6
9909 5
9909 65
9915 11
9915 245
9921 1
9945 1
9945 3
9945 16
9951 75
9957 2
9975 8
9975 11
9975 17
9975 61
9981 1
9987 4
9987 6
9987 18
9999 81
10005 4
10011 1
10011 61
10017 40
10017 112
10017 184
10023 32
10029 3
10035 9
10041 5
10047 4
10047 40
10059 3
10059 7
10059 9
10059 39
10065 199
10083 24
10083 104
10101 15
10107 2
10107 38
10125 92
10131 3
10131 13
10131 39
10137 70
10143 4
Citrix is offline   Reply With Quote
Old 2007-06-24, 07:38   #3
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

3×7×487 Posts
Default

Thanks, Citrix, for adding to my list. I think it's great to have a comprehensive list of all primes and twin primes of certain forms up to certain limits of k and n before going after the really big primes.

For my list, I unofficially tested k=1 to 600 (i.e. ran no programs) up to the lower limit of where primes were tested to on the Riesel and Proth search sites by matching up the k's and n's. This has usually been up to at least n=200K because both Riesel and Proth primes have been mostly tested at least that high for all k's < 600. So I think doing any further twin testing for k < 600 would not be worthwile because even trying to find one twin above n=200K would take months and possibly years without a large coordinated effort.

I have 3 decent-speed machines working on other prime efforts right now that I want to continue on for several weeks yet and a very slow older machine that I use for sieving while the others are prime testing. I think I'll do 3 things here to continue this process:
1. Specify exactly how far each of the k's on my list have been tested. Yours are specifically tested to n=250, but I can't say for sure how high of an n each k is tested on mine without looking more closely at the various sites.
2. Add your primes to my list.
3. Once my slow-speed machine (333 mhz) is done with it's current sieve in about 2 days, I'll use it to test your k's to higher n's for twins. As slow as it is, I'll either limit the n's to 1000 or limit the k's to 2000 and allow the n's to go up to 10000 or so. Obviously these are very rough estimates only.

Also to be determined for my list...what gaps exist in the primes for the k's listed on the RPS, i.e. 15k, site, the Primesearch site, and the Proth search site. It's not immediately obvious where gaps exists. One gap that I know of for sure on Riesel primes is for k=289 from n=300K to n=501991. I checked around on another area in this forum and no one could say for sure that the range had been tested so I reserved it. I currently have my highest-speed dual-core machine working on the entire range. Any other Riesel prime that I find in that range will also be tested for a twin or checked for the same n on the Proth search site.


Gary
gd_barnes is online now   Reply With Quote
Old 2007-06-26, 08:19   #4
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

237638 Posts
Default Combined list with testing limit included

Citrix,

Actually, k=1 to 600 have been searched enough since that's how far the Proth search site goes up to and so is how far up I matched the site with ours.

I wasn't able to do any more testing yet but I combined your list with mine and added the value of n that each k has been tested through. Of course all of yours are 250. I also added odd k's divisbile by 3 (i.e. k=3 mod 6) up to k < 1000 where no twins were found and showed (none) by them. People might like to test those with a little more vigor in the future. I suspect there will be plenty of k's that have no twin primes found. It will be interesting to see if the lowest value of k=3 mod 6 where there are no twins really turns out to be k=111 like it is now. It has technically been tested to n=350K.

I should be able to extend the search for k > 600 a little on Tuesday sometime. Thanks for your help so far. This might turn out to be an interesting effort and could give us a good base to work from if we wish to find somewhat large triplets, quadruplets, 5-tuples, etc. in the future.

My changes are attached.


Gary
Attached Files
File Type: txt twin primes match.txt (24.7 KB, 377 views)

Last fiddled with by gd_barnes on 2007-06-26 at 08:22
gd_barnes is online now   Reply With Quote
Old 2007-06-28, 04:19   #5
Citrix
 
Citrix's Avatar
 
Jun 2003

157510 Posts
Default

Twins upto n=500. These twins are really rare..

165 264
165 282
555 282
573 344
615 391
669 333
969 269
1023 380
1215 255
1701 387
1743 418
1899 291
1995 492
2085 455
2373 294
2475 260
2565 468
2667 288
2805 259
3321 371
3381 281
3921 443
4101 443
4323 458
5049 361
5139 251
5253 338
5415 435
5547 470
6405 299
7173 294
7503 488
7605 314
7785 355
7791 331
8613 458
8787 472
9063 456
9129 359
9345 445
9369 365
9543 310
9609 297
9789 263
9951 257
9993 308
10071 327
Citrix is offline   Reply With Quote
Old 2007-06-28, 04:35   #6
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

3×7×487 Posts
Default Complete twin list k=1-100K and n=1-5K

Attached is a complete list of all twin primes for k = 1 to 100K and n = 1 to 5K for the form k * 2^n +/- 1. It also includes the twin 459 * 2 ^ 8529 +/- 1 from my earlier effort to match up all known Riesel and Proth primes. There are a total of 17717 twins in the list.

I hope someone finds this useful in searches for more 'exotic' primes such as triplets, quads, 5-tuples, etc.

Eventually I want to expand the list for all k < 1M and all n < 100K. If anyone wants to contribute to the effort, let me know. I'll be sieving to n=10K later this week, which won't take long.

n's > 66K make the current top-20 twin prime list.


Gary
Attached Files
File Type: txt twin primes k=1-100K n=1-5K.txt (224.3 KB, 549 views)

Last fiddled with by gd_barnes on 2007-06-28 at 05:05
gd_barnes is online now   Reply With Quote
Old 2007-06-28, 05:02   #7
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

3×7×487 Posts
Default How sieving multiple k's and n's on twins ?

Quote:
Originally Posted by Citrix View Post
Twins upto n=500. These twins are really rare..
Sorry we duplicated efforts there Citrix. Yes, twins are rare, which makes them special. Imagine triplets or quads! I checked my new extended list and all of yours are on there.

I'm curious...how are you sieving multiple k's and n's on twins? Here's what I'm doing but I'm thinking there must be a better way:

1. Use NewPGen and have it increment the n by 1 each time after it searches the range of k (in my case was 1 to 100000) that I want. For n < 2500, I just let it do each n almost instantly by sieving to only 1M since LLR is finding them rapidly. For n > 2500, I sieved to 100M. But these were just guesses because of the problem in #2.

2. #1 has the annoying problem of creating 1 file for each n, which I can't seem to get around. So I'm forced to then copy all of the files into one big file. I've been doing them 500 n's at a time.

3. Fortunately LLR, being the great program that it is, is able to accept one big file with many lines of XXXX:T:0:2:3 throughout the middle of it so it's able to handle many k's and n's in the same file.


I found the above to still be far faster than attempting to use the very slow Proth program and letting it both sieve and find primes. Do you know of a faster (or at least cleaner) way to sieve multiple k's and n's into one file? If there's some other software out there that would be better, could you provide a link to it? I get all of these various sites confused at times.

It doesn't take too long to copy 500 files into 1 file and then delete the 500 files. But the main problem with it only sieving 1 n at a time is that I can't get an accurate estimate of how many primes are being removed per second. I mean for 1 n, it might be removing only 1 per second but if it were sieving all 500 n at once, it might be removing 500 per second. But I don't know yet because in only sieving to 100M, it finishes fast enough that it doesn't show the rate. I finally resorted to just writing down the starting and ending time on my watch to determine how much total sieving and LLR time it was taking for each range of 500 n to get an idea of when to increase my sieve limit.


Thanks,
Gary
gd_barnes is online now   Reply With Quote
Old 2007-06-28, 20:37   #8
Joshua2
 
Joshua2's Avatar
 
Sep 2004

13×41 Posts
Default

What is the goal of all this? Is it supposed to help the TPS project some way? I don't quite get what you guys are doing.
Joshua2 is offline   Reply With Quote
Old 2007-06-29, 06:56   #9
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

100111111100112 Posts
Default It's in the process

Quote:
Originally Posted by Joshua2 View Post
What is the goal of all this? Is it supposed to help the TPS project some way? I don't quite get what you guys are doing.
What is our goal? We're finding twin primes! I believe the goal of these forums is to find all of the primes of certain forms; not just the large ones. Our goal here is to find all of the TWIN primes of a certain form. Some people prefer to find very few large primes. We here prefer to find all of the small primes and gradually build our way up to the large primes. Since very few people are interested in this sort of 'dirty work', that is our task here. This is no different than our < 300 site. It doesn't show just large primes, it shows them all.

The great 19th-century mathematician Carl Friedrich Gauss didn't start trying to manually calculate prime numbers beginning at 1 billion or higher just to make a big splash or set some sort of calculation record. He painstakingly started where others had left off and manually calculated ALL primes up to 3 million in order to construct some of the greatest mathematical proofs and theories of all time.

It is only in the painstaking process of starting with the elementary building blocks of a process that one can glean the information needed in order to gain a deeper understanding of the process as a whole.




Gary

Last fiddled with by gd_barnes on 2007-06-29 at 07:27 Reason: spelling/grammar
gd_barnes is online now   Reply With Quote
Old 2007-07-03, 20:39   #10
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

3×7×487 Posts
Default List of twins completed to n=10K

I've completed searching for twins up to n=10K for k=1 to 100K. The list is attached. There are only 23 twins between n=5K and 10K. I can see that I'm going to need to expand the list up to k=1M or 10M to get any significant # of twins for n>10K. (no surprise there!)

I also checked the list for triplets and quadruplets. The largest of all 3 kinds that I've found so far are:

Twins: 33891*2^9869-1,+1

Triplets: 32811*2^2707-1,+1,+5

Quads: 3741*2^153-1,+1,+5,+7

I also checked triplets and quads for the form of k*2^n-7,-5,-1,+1 and k*2^n-5,-1,+1 but there were none as large.

-7, -5, +5, and +7 primes were checked at http://www.alpertron.com.ar/ECM.HTM. The largest ones were also checked with Primo software.

Although the list looks small now, it only takes an exponent of 10475 to make the top-10 triplets list and an exponent of 3489 to make the top-10 quads list. Largest k-tuplets are shown at www.ltkz.demon.co.uk/ktuplets.htm.


Gary
Attached Files
File Type: txt twin primes k=1-100K n=1-10K.txt (214.7 KB, 398 views)
gd_barnes is online now   Reply With Quote
Old 2007-08-21, 02:40   #11
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

3·7·487 Posts
Default TPS extended to n=15K up to k < 1M.

I have now extended the Riesel-Proth twin prime search up to n=15K for all k < 1M.

I am attaching two lists:
1. The original list for k < 100K extended to n=15K sorted by k. 8 additional twins were found at this low level of k. To find them easily, you'll probably need to look at the list in #2.

2. A new list for k < 1M for 10K < n <= 15K sorted by n. There were a total of 85 twins in this range. Note that it includes the 8 twins from #1.


The most interesting find was 915 * 2 ^ 11455 +/- 1. It is the only twin that I've seen where k is < 1K and n is > 10K. In doing a search of the top-5000 site archives for twins, I see that it has already been found but there are none greater for k < 1K. A further analysis of the top-5000 archives shows that 80 of these 85 twins were never stored there so there is plenty of new information here.

I did tests for both +5 and -5 triplets on all 85 new twins. None were found. Eventually it would be interesting to extend the k to 1M for n < 10K and see if some higher triplets or quads can be found then what was posted last time but NOT to list more small twins. The chances are slim that a triplet or quad will be found for k < 1M for n > 15K.

I am now sieving for twins in the range of 15K < n <= 20K and k < 1M.


Gary
Attached Files
File Type: zip twin primes n=1-15K.zip (61.7 KB, 235 views)
gd_barnes is online now   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Sieving with powers of small primes in the Small Prime variation of the Quadratic Sieve mickfrancis Factoring 2 2016-05-06 08:13
Relativistic Twins davar55 Science & Technology 68 2015-01-20 21:01
3x*2^n-1 and 3x*2^n-1 possibly twins ? science_man_88 Riesel Prime Search 10 2010-06-14 00:33
The Twins GP2 Lounge 1 2003-11-18 04:50
NOT twins graeme Puzzles 11 2003-09-04 00:41

All times are UTC. The time now is 02:05.

Mon Oct 26 02:05:57 UTC 2020 up 45 days, 23:16, 0 users, load averages: 2.02, 2.04, 1.83

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.