Twin Mersenne Primes

[ewmayer]

Originally Posted by TTn

You almost have a point, in that technically all properties of numbers lay beyond mankinds boundries, ie 99.999...% of them.(Guys law of numbers)

He more than "almost has a point" - he's absolutely right, and you're wrong.

But If there is a known mod, then we can safely say that there can be no other primes. This is the case as is proven with RMA.

What do you mean by "known mod?" What do you mean by "RMA"?

I'll break it down in my next message.

Still waiting ...

I have replied in detail about the math, but the message did not get sent through.

Ewmayer,
Shoot first
Ask questions later.

That type of response doesn't really deserve re-post.
But simply put the "known mod" = base, in the algorithm.(2)
Understanding the expression algorithm,
will give you a better insite on the precious Mersenne primes.

Mersenne prime exponents are the sum of all the times k, was divisable by base=2 during the entire algorithm to that point, of general Mersenne primes.
k & n = prime
4 0 = 3
2 2 = 7
4 3 = 31
4 5 = 127
10 7 = 1279
14 8 = 3583
10 9 = 5119
6 10 = 6143
4 11 = 8191 two is a factor of k, 13 times.
The exponents of two, from k on the left, are added to n on the right,
p = 2+1+2+2+1+1+1+1+2 = 13
This is true of any candidate's exponent, gM or Mn for that matter.

[philmoore]

Originally Posted by TTn

I have replied in detail about the math, but the message did not get sent through.

Ewmayer,
Shoot first
Ask questions later.

That type of response doesn't really deserve re-post.

I'm sorry, but I thought this was a little out of line. Ewmayer's first post (in the other thread) politely expressed a genuine interest in what you had to say but simply pointed out that he hadn't yet seen the explanation that you were promising. I understand your frustration that your post was lost, but that really was not Ernst's fault.

I'm sorry, but I thought this was a little out of line. Ewmayer's first post (in the other thread) politely expressed a genuine interest in what you had to say but simply pointed out that he hadn't yet seen the explanation that you were promising. I understand your frustration that your post was lost, but that really was not Ernst's fault.

How are you trying to put that spin on it?

politely expressed a genuine interest in what you had to say

This is not spun as genuine interest.

Ewmayer He more than "almost has a point" - he's absolutely right, and you're wrong.

The shoot first

Then he asks questions reguarding the validity of the claim, for which he has already cast out of his mind prematurely.

What do you mean by "known mod?" What do you mean by "RMA"?

The asking questions later.

I am perfectly in line, with the linear succession of his reply.
I didnt blame him at all for the lost message, if that's what you imply.

[ewmayer]

Originally Posted by TTn

Mersenne prime exponents are the sum of all the times k, was divisable by base=2 during the entire algorithm to that point, of general Mersenne primes.
k & n = prime
4 0 = 3
2 2 = 7
4 3 = 31
4 5 = 127
10 7 = 1279
14 8 = 3583
10 9 = 5119
6 10 = 6143
4 11 = 8191 two is a factor of k, 13 times.

Why do you write 2 as 2*2^2 - 1, but 8191 as 4*2^11 - 1? If one instead writes 8191 as 2*2^12 - 1 one gets a different sum.

again my lengthy message vanishes into thin air. EERAAAARGGGHHHH..

Again, again!!!!!

Ewmayer, that is not the algorithm. 8191 as 2*2^12-1 would imply that the last prime found was 1*2^12-1.

k & n = prime
4 0 is reset as 1 2

2 2 is reset as 1 3
2 3 is composite

4 3 is reset as 1 5
2 5 is composite

4 5 is reset as 1 7
2 7 is composite
4 7 is composite
6 7 is composite
8 7 is composite

10 7 is reset as 5 8
6 8 is composite
8 8 is compoiste
10 8 is composite
12 8 is composite

14 8 is reset as 7 9
8 9 is composite

10 9 is reset as 5 10

6 10 is reset as 3 11

4 11 = 8191 two is a factor of k, 13 times.


It's pretty damn cool!
The residue of all general Mersenne primes is responsible for Mersenne prime exponents, or Mn for that matter.

[masser]

Originally Posted by Bob Silverman

One can't even
begin to talk about whether there are infinitely many Mersenne primes without
at least knowing basic probability and the definition of a probability density
function. One can't properly discuss a subject without knowing the
language.

Are you sure that the proof that there are infinitely many Mersenne primes will require the definition of a probability density function? The proof that there are infinitely many prime numbers doesn't require any such definition.

With all due respect,
masser

[ewmayer]

TTn, you should consider composing your lengthier messages off-line in a text editor, or making sure to copy the body before clicking the "submit" button. Like you, I learned that the hard way.

Originally Posted by TTn

Ewmayer, that is not the algorithm.

Yes - I'm trying to figure out what the algorithm IS, since you've not (at least to my caffeine-deprived mind) spelled it out precisely.

You consider a sequence of numbers of the form k*2^n - 1. You then do some manipulations (what precisely happens during a "reset"?) on k and n. k apparently need not be prime, but k somehow involves a power of 2 that is determined by the preceding term(s) of the sequence, but it's still not clear to me what rule you're using, since you first say "Mersenne prime exponents are the sum of all the times k, was divisable by base=2 during the entire algorithm to that point, of general Mersenne primes" but then you never state formally how one is to write k. So please indulge my dumbness, and give us a formal, PRECISE description of your algorithm, i.e.:

* What determines the starting values of k and n?

* In what order does one cycle through the generalized-Mersenne sequence?

* How are k and n incremented (or decremented) as one cycles through the sequence? In particular, what determines the power of 2 that appears in k?

*Make sure to copy the body before clicking the "submit" button.

I did that last time and prevailed.(wind0z settings still correct and all)

*(what precisely happens during a "reset"?) on k and n.

reset:
The expression change is implemented only when a prime is found. "the heart of the algorithm".
Expression change, just checks to see how many times k, is divisable by 2 and divides them out.
Then places them into their proper index(exponent)
When the base is even, k's lowest expression is odd.
When the base is odd, k's lowest expresstion is even.

*k apparently need not be prime.

Bingo! nor n, but they connect the Mersenne prime exponents.
Check it out on a logarithmic graph. ( gM up to M1279 below)

*You never state formally how one is to write k.

k is written as a multiple of two, unless it is found prime then k, is reset to an odd residue.
The next k's to look at will be k+1, k+3, K+5, and so on....
It makes for easy scripting input for newpgen and LLR.
Here is the largest known gM prime:
16371*2^216098-1
16372 is composite
16374 is composite
...
Ofcourse these composites have already been sieved out, from the previous reycyling.
Let me explain that a little more, an advantage of the algorithm
is FAST fixed n sieving, where the file is recycled each prime found.
Technically this a new "Anchored k sieving procedure" (HIGHLY EFFICIENT!!!)
since k stays as small as possible relatively speaking.

So please indulge my dumbness,

No need to patronize,...
lol We all know that ewmAYER.dumb = false.

* What determines the starting values of k and n?

By default Mersenne primes are always a good starting point, k=1 n=prime
Otherwise you must know that it is a general Mersenne prime, that's been carried from a gM.
There may be other strategies though.

* In what order does one cycle through the generalized-Mersenne sequence?

Linearly until a prime is found, end cycle.
This applies to jumping into the sequence as well from any unknown Riesel prime.
You could execute the algorithm, and find yourself quickly merged back into the gM sequence.

* How are k and n incremented (or decremented) as one cycles through the sequence? In particular,
what determines the power of 2 that appears in k?

K is incremented by 2, in this case because we are dealing with a base 2 expression.
If we were looking at k*3^n-1, we would increment k by 3.
k is decremented when a prime is found only.

Anyways we increment k by 2, > spawning from the lowest expression of the last prime found.

Here are their lowest expressions.
1 2
1 3
1 5
1 7
5 8
7 9
5 10
3 11
1 13
5 14
1 17
1 19
7 21
13 23
39 24
11 26
1 31
5 32
3 34
3 38
25 39
3 43
7 45
5 48
19 49
11 50
21 51
5 54
3 55
1 61
3 64
67 65
63 66
43 67
63 68
5 72
15 73
3 76
55 77
47 78
15 80
15 82
1 89
3 94
17 96
9 99
3 103
1 107
9 109
75 111
35 114
15 116
45 117
45 119
27 121
27 122
1 127
95 128
115 129
55 131
19 133
11 134
75 136
87 138
3 143
15 145
5 148
17 150
145 151
39 153
25 155
15 157
9 159
27 160
25 161
65 162
19 165
321 166
51 169
27 170
15 172
69 173
35 174
7 177
131 178
5 184
69 185
19 189
33 190
63 191
65 192
45 193
51 195
155 196
83 198
15 202
3 206
33 208
9 211
3 216
79 217
377 218
349 219
15 224
25 225
135 226
169 227
317 228
173 230
229 231
69 233
31 235
117 236
75 237
51 238
273 239
149 240
23 244
11 246
5 248
17 252
27 253
155 254
45 256
35 260
23 264
15 266
5 270
21 271
5 274
165 275
255 276
159 277
49 279
181 281
165 282
103 283
13 287
15 289
13 291
15 293
41 294
87 296
63 298
69 299
91 301
3 306
9 309
411 310
69 313
203 314
57 317
3 324
45 327
27 329
33 330
199 331
25 335
297 336
165 338
9 343
363 344
457 345
229 347
75 349
55 351
11 354
17 356
33 360
11 362
181 363
195 364
267 365
143 366
129 368
199 369
231 370
273 371
121 373
117 374
65 376
69 377
35 380
33 382
81 383
3 391
123 392
19 395
115 397
893 398
669 399
189 401
221 402
495 403
707 404
429 405
31 409
71 410
45 411
9 415
5 420
121 421
161 422
83 424
105 426
391 427
399 428
375 429
533 430
375 431
175 433
171 434
91 435
119 436
301 437
237 438
481 439
63 443
117 445
145 447
143 448
397 449
27 454
3 458
17 460
15 463
45 466
3 470
55 471
85 473
153 474
541 475
117 478
319 479
173 480
225 481
27 485
53 488
325 489
229 491
329 492
231 493
125 496
27 500
33 503
795 504
153 507
647 508
111 511
243 512
157 513
87 514
1 521
681 522
439 523
585 524
397 525
21 530
107 532
291 533
657 534
1035 535
669 536
375 537
69 540
23 544
189 545
297 546
243 548
83 550
41 554
155 556
513 558
293 560
85 563
77 566
139 567
69 569
27 574
45 577
333 578
49 581
41 582
199 583
97 585
135 586
265 587
45 591
843 592
275 594
115 597
261 598
1 607
113 608
17 612
225 613
113 614
133 615
105 617
135 618
679 619
447 621
115 623
2163 624
1197 625
511 627
317 628
621 629
301 631
25 635
41 638
93 639
53 642
287 644
159 647
19 651
17 654
87 656
165 657
243 658
17 664
19 665
395 666
167 668
147 669
153 671
177 672
181 673
83 676
67 677
581 678
87 682
35 686
25 687
339 688
309 689
343 691
235 693
197 694
17 698
17 702
539 704
937 705
855 706
565 707
905 708
597 709
57 713
63 714
61 715
111 718
395 720
205 721
165 722
183 724
213 726
423 727
309 728
231 729
635 730
177 732
51 735
31 739
377 740
727 741
393 742
201 743
335 744
143 746
123 747
537 748
1009 749
917 750
751 751
261 754
273 755
41 758
63 759
317 760
415 763
139 765
43 767
19 771
129 773
411 774
453 775
9 781
407 782
1155 783
635 784
459 785
153 787
285 788
417 789
13 795
19 801
229 803
255 804
49 807
65 808
139 811
39 813
35 814
33 815
1355 816
223 819
3 827
205 829
273 830
1083 831
717 832
31 837
39 839
139 841
291 842
159 844
53 846
333 848
205 849
395 850
233 852
219 853
921 854
107 858
395 860
161 862
811 863
205 865
91 867
9 871
257 872
189 875
177 877
267 878
87 881
85 883
51 885
31 887
23 888
21 891
27 892
61 895
105 896
531 897
279 899
45 902
83 904
35 906
69 909
2207 910
1635 911
849 912
221 914
59 916
91 917
347 918
19 923
171 925
45 928
65 930
363 931
479 932
277 933
237 934
9 939
107 940
81 941
45 946
11 950
19 953
93 954
249 956
195 958
27 962
1479 963
685 965
213 967
75 969
17 972
237 973
131 974
553 975
147 977
287 978
153 979
273 980
141 983
719 984
495 985
515 986
471 987
317 988
711 989
465 991
1287 992
451 995
175 997
15 1004
985 1005
253 1007
479 1008
161 1010
1033 1011
319 1013
413 1014
113 1016
383 1018
295 1019
315 1021
61 1025
493 1027
329 1028
265 1029
177 1032
751 1033
33 1038
169 1039
277 1041
681 1042
173 1044
997 1045
67 1049
333 1050
693 1051
563 1052
387 1053
231 1054
69 1057
63 1059
359 1060
265 1061
429 1063
207 1065
405 1068
323 1070
199 1071
1117 1073
2567 1074
2121 1075
1097 1076
465 1078
235 1079
69 1081
167 1082
285 1083
255 1084
199 1085
843 1086
1335 1087
181 1091
1077 1092
541 1093
409 1095
437 1096
1891 1097
645 1099
61 1103
177 1104
123 1106
199 1107
241 1109
557 1110
1275 1111
797 1112
257 1114
655 1115
975 1116
415 1119
315 1120
401 1122
369 1124
657 1125
453 1126
309 1127
909 1128
115 1131
1667 1132
369 1135
409 1137
165 1139
411 1141
23 1146
181 1147
297 1148
451 1149
861 1150
329 1152
1095 1153
529 1155
1035 1156
387 1158
45 1162
73 1167
63 1168
43 1171
129 1173
585 1175
177 1177
61 1179
111 1181
447 1182
17 1188
69 1189
73 1191
449 1192
35 1196
199 1197
657 1198
531 1199
421 1201
2367 1202
665 1204
503 1206
27 1213
77 1214
59 1216
267 1217
2085 1218
1249 1219
321 1221
133 1223
717 1224
407 1226
1035 1228
1875 1229
941 1230
525 1231
285 1232
85 1235
99 1237
551 1238
177 1242
15 1246
75 1247
55 1251
405 1252
111 1255
773 1260
477 1262
197 1264
171 1265
3 1274
1 1279

Still waiting...


Correction, I had some merge bugs, with my program.
This may not be indeed a general Mersenne prime.
16371*2^216098-1

The problem is fixed(RMA Version 1.7)
This made me include a new option for multiple sieving of fixed n, that are also equal to the current gM candidate file.
The scripting process, is in progress now while I am figuring out, by testing the optimum values of time per n's that match the criteria.

Ewmayer,
Do you understand?
I noticed you've posted elsewhere since, but not replied here.
Maybe you are still checking it's validity... "in genuine interest."


"If you dont have anything bad to say, then dont say anything at all."