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2016-09-28, 20:41   #23
GP2

Sep 2003

32·7·41 Posts

Quote:
 Originally Posted by Raman Still wondering how that extremely smooth ECM curve prime factor or ECM curve prime number had been found out. [...] I doubt that if it were really found out by using ECM curves! Neither Prime95 ECM curves nor GMP-ECM ECM curves would have been able to be found it out. Right?
If you google the number 493613348917766417426006591803225943649556875046256846631045789294232301761, you find this old thread: "Faking factors with Complex Multiplication", and within that thread post #4 discusses that number. It does seem it was found artificially, if I understand that post correctly.

Quote:
 Originally Posted by Raman Windows version of Prime95 does not use up with the PRP tests for the type of the work outs to be assigned with the select option from the combo box at all. Right? They need to be only manually entered from the worktodo.txt file or what? Linux / Unix version of mprime only accepts with the inputs from worktodo.txt file manually entered or automatically assigned. Do they not have with the graphical user interface or the menu styles for the type of the work outs to be assigned with the select option from the combo box? They are only menu styles!
Primenet doesn't assign PRP tests or accept PRP test results. Prime95 can do PRP testing, but it can't be selected from any menus, you have to manually add lines to a worktodo.txt file. But you have to be careful, because any PRP results you obtain have to be manually reported to mersenne.ca (NOT mersenne.org) by copying and pasting the lines from results.txt, otherwise those results will be lost.

You can obtain PRP assignments from mersenne.ca at this page at mersenne.ca by clicking on a link in the rightmost "Assignments" column. Those pages don't really give any instructions, which is unfortunate.

2016-09-28, 20:43   #24
GP2

Sep 2003

32·7·41 Posts

Quote:
 Originally Posted by axn GMP-ECM uses a completely different stage 2 algorithm from P95 (something like O(sqrt(B2)) vs O(B2)). It is hugely (yuugely!) more memory-intensive, but can attain much higher B2 in the same time.
I think GMP-ECM can only be used on rather small exponents. What is the limit in practice for the largest exponents that you would attempt with GMP-ECM?

 2016-09-28, 22:06 #25 lycorn     Sep 2002 Oeiras, Portugal 23·181 Posts Sometime ago I ran a couple of curves on different exponents and B1/B2 bounds and came to the conclusion that using Prime95 for Stage 1 and GMP-ECM for Stage 2 pays for exponents up to ~40K, but the smaller the exponent the more significant the gains are. I´m still using that combo for very small exponents (1277, for one). May be Santa will drop something down my chimney, who knows?...
2016-10-07, 10:06   #26
Raman
Noodles

"Mr. Tuch"
Dec 2007
Chennai, India

100111010012 Posts

Quote:
 Originally Posted by Raman Order Sorted Up Away out off up down my own. Of with that that this is always existing out! My own. Away out off up down. Of with that that this is always existing out!
77. 2172759-1 has a factor: 672002676922157179283240771609
Fingers crossed up - keep up stay away...!

Quote:
 Originally Posted by Raman Tension = Stress? Ratio ration approximation factor rate - where ever as like! Of for from front frontier - of of just that is being - rather than instead of - in to the before wards after wards to wards over there by - of with but that that - of that which that this!
Good enough in to the have got been results per month statistics!
Good enough in to the have got been Mersenne prime number exponents per 1000000 statistics - of the following form - where ever as like!
Good enough in to the have got been age per days statistics!

 2016-10-13, 11:00 #27 Raman Noodles     "Mr. Tuch" Dec 2007 Chennai, India 3·419 Posts 78. 21408087-1 has a factor: 2138342186768010337729. $ \begin{tabular}{|l|l|l|l|l|l|l|} \hline CPU\ Name & Exponent & Result\ Type & Received & age\ days & Result & GHz-Days \\ \hline Ajith & 1408087 & F-ECM & 2016-10-11\ 09:55 & 4.1 & 2138342186768010337729 & 0.0471 \\ \hline Michael & 172759 & F-ECM & 2016-10-05\ 12:02 & 0.9 & 672002676922157179283240771609 & 0.1395 \\ \hline Alex\ Pandian & 1400251 & F-ECM & 2016-09-26\ 08:36 & 2.0 & 2190658775806151479217 & 0.0471 \\ \hline Michael & 158209 & F-ECM & 2016-09-20\ 10:57 & 5.9 & 26496805856040782582748460014520511 & 0.1392 \\ \hline Alex\ Pandian & 1413017 & F-ECM & 2016-09-02\ 07:56 & 1.0 & 2226694532490185824727 & 0.0943 \\ \hline Nithya & 1320091 & F-ECM & 2016-08-23\ 12:02 & 1.0 & 231827487452450337577 & 0.1160 \\ \hline Ajith & 1085809 & F-ECM & 2016-08-18\ 12:56 & 1.0 & 8381291184102382541497 & 0.0727 \\ \hline Ashok & 1420109 & F-ECM & 2016-08-10\ 11:08 & 2.2 & 85148369868485192804575096841 & 0.0472 \\ \hline Ajith & 1306477 & F-ECM & 2016-08-04\ 05:26 & 2.6 & 2886593156080095874622681 & 0.1158 \\ \hline Alex\ Pandian & 1264387 & F-ECM & 2016-07-28\ 10:17 & 1.0 & 111421197216700721651761 & 0.1152 \\ \hline Ajith & 1073647 & F-ECM & 2016-07-27\ 06:47 & 1.0 & 45496627768358111930287 & 0.1089 \\ \hline Ashok & 1297129 & F-ECM & 2016-07-20\ 10:37 & 1.9 & 21635389012955382990854233 & 0.0386 \\ \hline Ajith & 1249741 & F-ECM & 2016-07-08\ 11:30 & 1.1 & 168691067410297172399521 & 0.1150 \\ \hline Gokul\ Nath & 1415957 & F-ECM & 2016-07-06\ 12:50 & 1.2 & 49084592298749387589959 & 0.0943 \\ \hline Ashok & 1205173 & F-ECM & 2016-07-02\ 12:12 & 1.2 & 269867708244063132649 & 0.0763 \\ \hline Nithya & 1335563 & F-ECM & 2016-07-01\ 11:43 & 1.1 & 1059938762839012963385177 & 0.0934 \\ \hline Ajith & 1110167 & F-ECM & 2016-06-30\ 08:49 & 1.0 & 14693675794413895601977 & 0.1094 \\ \hline Rajesh & 1185697 & F-ECM & 2016-06-29\ 11:43 & 3.0 & 103519616241334574089 & 0.1104 \\ \hline Ashok & 1185319 & F-ECM & 2016-06-28\ 07:33 & 2.8 & 187769929174579865730719 & 0.1141 \\ \hline Manual\ testing & 680077 & F-ECM & 2016-06-27\ 06:38 & 0.0 & 359004574534541931650318449 & 1.1078 \\ \hline Alex\ Pandian & 1406857 & F-ECM & 2016-06-25\ 06:24 & 1.0 & 76972723442421389411833 & 0.1413 \\ \hline Ignasi & 1103281 & F-ECM & 2016-06-22\ 13:08 & 1.2 & 461658571972334163101951 & 0.1056 \\ \hline Sri\ Sridhar & 1082533 & F-ECM & 2016-06-16\ 07:38 & 1.8 & 1623069162917486699809 & 0.0727 \\ \hline Nithya & 1001629 & F-ECM & 2016-06-14\ 06:35 & 4.9 & 25980809010119884941817 & 0.0901 \\ \hline Manual\ testing & 679669 & F-ECM & 2016-06-10\ 04:52 & 0.0 & 63260117764832948321737 & 0.8308 \\ \hline Gokul\ Nath & 1409633 & F-ECM & 2016-06-09\ 08:47 & 1.1 & 4562270691505620280350953 & 0.1413 \\ \hline Sri\ Sridhar & 1314161 & F-ECM & 2016-06-06\ 08:45 & 2.0 & 200209995939544733759 & 0.0386 \\ \hline Ajith & 1401767 & F-ECM & 2016-06-03\ 15:14 & 1.1 & 208164200904253362898039 & 0.1412 \\ \hline Ignasi & 1309811 & F-ECM & 2016-06-03\ 11:38 & 1.2 & 6452094516571781903870908529 & 0.1159 \\ \hline Ajith & 1212769 & F-ECM & 2016-06-03\ 08:33 & 1.0 & 22686603584990095872353327 & 0.1108 \\ \hline Nithya & 1155919 & F-ECM & 2016-05-30\ 13:12 & 3.1 & 2446997794177577666902847 & 0.0367 \\ \hline Manual\ testing & 674483 & F-ECM & 2016-05-27\ 12:31 & 0.0 & 1185762874913395945847 & 1.1066 \\ \hline Sri\ Sridhar & 1151041 & F-ECM & 2016-05-26\ 08:32 & 2.0 & 98338208354439540871 & 0.0367 \\ \hline Ajith & 1389149 & F-ECM & 2016-05-26\ 05:52 & 1.6 & 1968838610224783811144921 & 0.0940 \\ \hline Ajith & 1362349 & F-ECM & 2016-05-25\ 12:13 & 2.0 & 4052494766327711626877807 & 0.0468 \\ \hline Manual\ testing & 640483 & F-ECM & 2016-05-25\ 07:23 & 0.0 & 35948758457297251395594732823879 & 1.0451 \\ \hline Nithya & 1238119 & F-ECM & 2016-05-24\ 05:48 & 1.0 & 19398358097550480988759 & 0.0370 \\ \hline Santhosh & 1361609 & F-ECM & 2016-05-23\ 18:14 & 0.4 & 8394136703834908414711 & 0.0468 \\ \hline Ignasi & 1381381 & F-ECM & 2016-05-23\ 07:29 & 2.8 & 486078017602417074080489 & 0.0939 \\ \hline \end{tabular}$ $ \begin{tabular}{|l|l|l|l|l|l|l|} \hline Michael & 130547 & F-ECM & 2016-05-21\ 14:18 & 1.2 & 740710078242573288550675295986147001 & 0.1387 \\ \hline Ajith & 1352543 & F-ECM & 2016-05-18\ 11:59 & 1.2 & 54914730373539406420367 & 0.0936 \\ \hline Ashok & 1048361 & F-ECM & 2016-05-17\ 14:09 & 4.3 & 317587687414956893560559 & 0.1049 \\ \hline Gokul\ Nath & 1062367 & F-ECM & 2016-04-29\ 09:31 & 1.0 & 5715626615941288867913951 & 0.0363 \\ \hline Nithya & 1209781 & F-ECM & 2016-04-29\ 07:00 & 1.0 & 61574197954768721757880409 & 0.1108 \\ \hline Manual\ testing & 614909 & F-ECM & 2016-04-28\ 09:44 & 0.0 & 2157432123233208899520343 & 0.8318 \\ \hline Suganya & 1017043 & F-ECM & 2016-04-28\ 09:21 & 1.9 & 2714087245272479000359 & 0.0903 \\ \hline Alex\ Pandian & 1403807 & F-ECM & 2016-04-28\ 04:21 & 1.6 & 910040398878981948860243369 & 0.0941 \\ \hline Sri\ Sridhar & 1151327 & F-ECM & 2016-04-27\ 09:41 & 1.0 & 374909084903502844569223 & 0.0733 \\ \hline Ignasi & 1394089 & F-ECM & 2016-04-23\ 09:20 & 1.0 & 12522193154648380174007 & 0.0940 \\ \hline Alex\ Pandian & 1049891 & F-ECM & 2016-04-22\ 14:15 & 1.2 & 14792762552601957907766311 & 0.0724 \\ \hline Manual\ testing & 619979 & F-ECM & 2016-04-18\ 09:06 & 0.0 & 39952445419572244259873 & 0.6245 \\ \hline Alex\ Pandian & 1244249 & F-ECM & 2016-04-16\ 09:23 & 1.2 & 440414964773453095807 & 0.1112 \\ \hline Suganya & 1176221 & F-ECM & 2016-04-11\ 11:58 & 3.9 & 461610300972747494021593 & 0.0735 \\ \hline Santhosh & 1030219 & F-ECM & 2016-04-07\ 12:50 & 1.0 & 3772589184204120078374871601 & 0.0301 \\ \hline Vijay & 1226387 & F-ECM & 2016-04-06\ 06:35 & 1.8 & 1074355317155260325278943 & 0.1147 \\ \hline Suganya & 1062793 & F-ECM & 2016-04-05\ 11:28 & 5.0 & 12513099136956335921312007791 & 0.1088 \\ \hline Ajith & 1023769 & F-ECM & 2016-04-05\ 07:02 & 2.8 & 121894953460427063046553 & 0.0602 \\ \hline Manual\ testing & 1196059 & F-ECM & 2016-04-04\ 10:30 & 14.1 & 17663439686039008542085063 & 0.1803 \\ \hline Alex\ Pandian & 1111949 & F-ECM & 2016-04-04\ 04:33 & 2.7 & 131359229602139901573898435183 & 0.0729 \\ \hline Sri\ Sridhar & 1328891 & F-ECM & 2016-04-02\ 12:48 & 1.2 & 190486443247254756345034440671 & 0.0933 \\ \hline Manual\ testing & 1198261 & F-ECM & 2016-03-31\ 10:39 & 9.1 & 186410816493618076522807 & 0.1203 \\ \hline Sri\ Sridhar & 1058077 & F-ECM & 2016-03-31\ 05:57 & 0.9 & 1155399346576072505554663 & 0.0362 \\ \hline Ajith & 1295611 & F-ECM & 2016-03-30\ 09:47 & 1.1 & 1538613486295112984311 & 0.1157 \\ \hline Manual\ testing & 1387681 & F-ECM & 2016-03-29\ 15:15 & 15.1 & 7635519794781065554162223 & 0.0874 \\ \hline Sri\ Sridhar & 1293421 & F-ECM & 2016-03-29\ 07:43 & 1.0 & 46804080444409785497993 & 0.1157 \\ \hline Suganya & 1094623 & F-ECM & 2016-03-26\ 09:04 & 2.2 & 7153958318333686172617 & 0.1092 \\ \hline Santhosh & 1409549 & F-ECM & 2016-03-24\ 10:24 & 1.0 & 6884935783696551152303 & 0.1413 \\ \hline Nithya & 1045487 & F-ECM & 2016-03-23\ 13:34 & 1.1 & 12870043214611775340199 & 0.1085 \\ \hline Nithya & 1196123 & F-ECM & 2016-03-22\ 11:05 & 1.1 & 25412328569397020505047 & 0.0369 \\ \hline Vijay & 1104017 & F-ECM & 2016-03-21\ 11:14 & 2.2 & 10390283462108941247777 & 0.0704 \\ \hline Gokul\ Nath & 1396529 & F-ECM & 2016-03-19\ 08:14 & 1.8 & 3430327700879658519722567 & 0.0941 \\ \hline Vijay & 1269167 & F-ECM & 2016-03-16\ 06:33 & 0.1 & 69389537933503942909169 & 0.0384 \\ \hline Ramakrishnan & 1357901 & F-ECM & 2016-03-15\ 12:16 & 4.0 & 4006306700470164867761 & 0.1404 \\ \hline Anushri\ Ayyappan & 1177741 & F-ECM & 2016-03-15\ 11:15 & 4.1 & 1393309518989601569849 & 0.0368 \\ \hline Priyanga & 1172207 & F-ECM & 2016-03-10\ 13:59 & 1.2 & 3612667936408840580839 & 0.0380 \\ \hline Manual\ testing & 683831 & F-ECM & 2016-03-08\ 10:21 & 0.0 & 817118841184883531740073 & 0.8315 \\ \hline Priyanga & 1342907 & F-ECM & 2016-03-05\ 09:08 & 0.2 & 3583767036379540468879 & 0.0467 \\ \hline TIS50-PC & 692779 & F-ECM & 2016-02-22\ 06:22 & 1.7 & 9113973384791662609433 & 0.0575 \\ \hline \end{tabular}$
 2016-10-13, 12:59 #28 Raman Noodles     "Mr. Tuch" Dec 2007 Chennai, India 23518 Posts Interesting to ask up with: always If I run away 5 ECM curves for each Mersenne number with no known prime factors exponents between 600000 and 700000 with B1 = 250000 and B2 = 128992510 and if TJOAI runs away 25 ECM curves for each Mersenne number with no known prime factors exponents between 600000 and 700000 with B1 = 50000 and B2 = 5000000 then what will be the chance that he would find out the same prime factor before wards of me doing it extracting up? For the factors of any size - at all - small or medium or large - any way some how every day Last fiddled with by Raman on 2016-10-13 at 13:19
2016-10-17, 16:08   #29
Raman
Noodles

"Mr. Tuch"
Dec 2007
Chennai, India

3·419 Posts

Suppose that if I run a lot of ECM curves stage 1 only up on say (2524287+1)/3 with B1 = 11000000 and store away their own same hexadecimal residues in to a text editor file case. With GMP-ECM or Prime95 will I be able to continue away with stage 1 only with those same their own stored away hexadecimal residues with B1 = 44000000 with those in to a text editor file case?

Quote:
 Originally Posted by Raman M1277 is that next Mersenne number with no known factors at all, after that only M1619. M1277 I guess that it may have a much larger enough prime factor, as it is closer to that prime number: M1279. Similarly as it was that case for M521, which is prime, M523 has a prime factor, that splits up into p69.p90
Why at Mersenne.org Exponent status web site page, query results are being limited to 1000 exponents?

Quote:
 Originally Posted by Raman By the way, why did Prime Net Server once assign one of single systems and then computers or machines for Trial Factoring assignment when I was looking out only for ECM curves on to smaller Mersenne composite numbers assignment?
A single of NF line, strangely and unusually sandwiched between a lot of F-ECM lines.

CPU Name: Karpov Michael Raj K.
Exponent: 135062611
Result Type: NF
Age Days: 1.7
Result: no factor from 270 to 271
GHz-Days: 1.7705

Quote:
 Originally Posted by Raman Please define what do you mean by semi-prime. I have heard of prime, but not semi-prime at all. Do you mean that it has got only two prime factors, with it actually? If so, M1063 & M881 are being semi-primes, as well, as is being the case for M523, M809, M727, M971, M983, M997. And then, I will define my own terms, as well. I will call 2*prime, a fraud prime, for this example, consider taking away with 3541-1, and then 5*prime, a cheat prime, 6271-1, as since 2 & 5 are alone being the trivial prime factors to be making the number composite, alone.
Already in its own best place,
at Mersenne.org ECM progress web site page not in its own synchronization with at Mersenne.org Exponent status web site page.

Quote:
 Originally Posted by Raman ECM on numbers like 21277-1, 21619-1, 21753-1, 22137-1, 22267-1, 22273-1, 22357-1, 22377-1, 22423-1, 22477-1, 22521-1, 22557-1, 22671-1, 22713-1, 22719-1, 22851-1, 23049-1, etc. will probably be totally futile without producing any useful results.
Prime numbers p below 10000 such that 2p-1 is composite but has got no known prime factors.
p ≤ 10000.

1277, 1619, 1753, 2137, 2267, 2273, 2357, 2377, 2423, 2477, 2521, 2557, 2671, 2713, 2719, 2851, 3049, 3673, 3691, 3847, 3881, 3919, 4007, 4049, 4111, 4159, 4261, 4363, 4567, 4583, 4591, 4703, 4721, 5443, 5471, 5503, 5839, 6007, 6073, 6247, 6581, 6679, 6733, 6763, 6971, 7069, 7127, 7321, 7351, 7621, 8291, 8329, 8369, 8389, 8581, 8681, 8923, 8999, 9011, 9227, 9463, 9473, 9551, 9679, 9857, 9929.

Much more larger prime factors are only being known recently, after wards when ever the Prime Net web site page server and client went automated after wards when ever.

Code:
1061: 46817226351072265620777670675006972301618979214252832875068976303839400413682313921168154465151768472420980044715745858522803980473207943564433.
1237: 2538207129840687799335203259492870476186248896616401346500027311795983.
1657: 10788426156438350117334292343137689257142387557947087583.
1669: 112493750443412941745410571996247741731544451845539488817.
2269: 5198395892876421104415109549087087419559080537214372111.
3607: 162160065980366340636967897279169391509046358190713.
4937: 224209400033890009931837488284049711636925260561.
5309: 4379627179880971499877583266262615461322386849281.
5879: 3381116440321017148580653633902983992991015840485797617951.
5923: 39615112643045557727531880705107806493554991.
6211: 1110196860540711188306812523817624319633363099818286801.
6329: 26367627467345446174566335936121340946860202281.
9209: 1821133994357721169773431211508950567060217.
9587: 6842693325161318357698161937504324710196297.
Text automatically adjusts itself to size of device and panel screen width.

Quote:
 Originally Posted by Raman A good observation... 21061-1 has got a prime factor of size = 143 digits. 1061 = Number of four-digit prime numbers 143 = Number of three-digit prime numbers If someone were to be being doing some research along this line, and then he / she would have certainly guessed it very much easily itself!
In contrast,

Open end aliquot sequences and series below 1000.
Starting element ≤ 1000.
All members.
Of side sequences and series.

276, 306, 396, 696
552, 888
564, 780
660, 828, 996
966

Quote:
 Originally Posted by Raman I would suggest the 2- table to be extended atleast upto that exponent of 1280. Note that 2,1237- 2,1277- have no factors at all after 2,1061-. The next is only 2,1619-, and that 2,1279- is prime, so that upto exponent 1280 would be fine enough! 1280 = 5.28 521, 523 are twin primes with M521 being prime, M523 has a large prime factor that is already being conquered. So, is the case with these twin primes 1277, 1279? Note that M1279 is a prime number, thus M1277 should have a large enough prime factor?
In contrast,

Open end aliquot sequences and series below 10000.
Starting element ≤ 10000.
Lowest members.
Of side sequences and series.

276, 552, 564, 660, 966, 1074, 1134, 1464, 1476, 1488, 1512, 1560, 1578, 1632, 1734, 1920, 1992, 2232, 2340, 2360, 2484, 2514, 2664, 2712, 2982, 3270, 3366, 3408, 3432, 3564, 3678, 3774, 3876, 3906, 4116, 4224, 4290, 4350, 4380, 4788, 4800, 4842, 5148, 5208, 5250, 5352, 5400, 5448, 5736, 5748, 5778, 6396, 6552, 6680, 6822, 6832, 6984, 7044, 7392, 7560, 7890, 7920, 8040, 8154, 8184, 8288, 8352, 8760, 8844, 8904, 9120, 9282, 9336, 9378, 9436, 9462, 9480, 9588, 9684, 9708, 9852.

Any patterns are being found out as like them?
Any progress in computations will be able to reduce these numbers down as like them they are being.
As like them, they are not being suitable enough for OEIS entries.
As like them, they are being applicable enough for T-shirt or formal shirt design patterns.

Code:
import java.lang.*;
import java.io.*;
// import java.util.*;
public class Results
{
public static void main(String args[])
{
try
{
RandomAccessFile file=new RandomAccessFile("results20161017.txt","rw");
RandomAccessFile W8191=new RandomAccessFile("W8191.txt","rw");
RandomAccessFile W19937=new RandomAccessFile("W19937.txt","rw");
RandomAccessFile W110503=new RandomAccessFile("W110503.txt","rw");
RandomAccessFile W524287=new RandomAccessFile("W524287.txt","rw");
// List l=new ArrayList<Integer>();
while(true)
{
if(s==null)
{
break;
}
else
{
String t=s.trim();
int i=t.length();
// if(!l.contains(i))
// {
// }
if(i>=262176&&i<=262179)
{
W524287.writeBytes(t+"\n");
}
else if(i>=55284&&i<=55287)
{
W110503.writeBytes(t+"\n");
}
else if(i>=10001&&i<=10003)
{
W19937.writeBytes(t+"\n");
}
else if(i>=4129&&i<=4131)
{
W8191.writeBytes(t+"\n");
}
}
}
// System.out.println(l);
}
catch(IOException e)
{
System.out.println(e.toString());
}
}
}
My own JAVA package distribution programming language scripting code.

For reading out results from results.txt text editor file case and then sorting them away in to the W8191.txt, W19937.txt, W110503.txt, W524287.txt text editor file case.

Quote:
 Originally Posted by Raman Hope that they will also be factored off sooner itself! M521 is prime, M523 had a larger sized factor. M1279 is prime, so that M1277 will thus have much larger enough factor?!
Mersenne Forum does not have colour for formatting code from
my own JAVA package distribution programming language scripting?

Quote:
 Originally Posted by Raman Consider with Mersenne Numbers of the following form 2p-1, there are being plenty of prime numbers of the following form 2kp+1 but only a few of them would divide 2p-1 such that their own product ≤ 2p-1. Due to a theorem of Number Theory, a prime number of the following form 2kp+1 should indeed obviously divide with 2kp-1. So that, 2kp+1 should divide with 2p-enπi/k for a some integer n such that 0 ≤ n ≤ 2k-1. For example, 367 = (2 × 3 × 61) + 1 neither divides with 261-1 nor divides with 261+1 but it should divide with 2366-1 = (261-1) × (261+1) × (2122-261+1) × (2122+261+1). Indeed 367 divides with (2122+261+1). For k = 1 case, this reduces in to if 2p+1 is being a some prime number for a some prime number p, then it should divide with either 2p-1 (when 2 is being quadratic residue (mod 2p+1), 2p+1 ≡ 1 or 7 (mod 8)), or divide with 2p+1 (when 2 is being quadratic non-residue (mod 2p+1), 2p+1 ≡ 3 or 5 (mod 8)). (p that is being Sophie-Germain prime number. 2p+1 is also being prime number too!)
Can zeros of Riemann Zeta Function be able to provide away us with any useful information about prime factors size or their own distribution when ever that it is being possible? Probably perhaps potentially.
Trivial zeros or non-trivial zeros.
Give away us with any productive information or hint or clue.

Quote:
 Originally Posted by Raman Quite very variably - about around - round ground - poultry variety. Away out up off down my own - that ever which ever a way a way - ever - by using be being - ever. Super Computer Words Order Sorted Up Away out off up down my own. Of with that that this is always existing out! My own. Away out off up down. Of with that that this is always existing out!
Questions and answers mode turning out in to the Report Results mode.
As like turning out in to the.
Attached Files
 W8191 231 ECM curves with B1 = 3e9, stage 1 residues 17 October 2016 Monday.tar.gz (280.3 KB, 109 views) W19937 462 ECM curves with B1 = 3e8, stage 1 residues 17 October 2016 Monday.tar.gz (1.31 MB, 128 views) W19937 924 ECM curves with B1 = 3e8, stage 1 residues 17 October 2016 Monday.tar.gz (1.31 MB, 123 views)

Last fiddled with by Raman on 2016-10-17 at 17:05

2020-07-14, 19:38   #31
sweety439

Nov 2016

22×3×5×47 Posts

Quote:
 Originally Posted by Raman I had to add up on with in a some of these prime factors for in to factordb.com web site page - for only of certainly ≤ 10000000 digits - limit range bound level - rate ratio scale proportion - exists out!
The Wagstaff Mersenne number (2170141183460469231731687303715884105727+1)/3 has a factor: 886407410000361345663448535540258622490179142922169401

Last fiddled with by Uncwilly on 2020-07-14 at 20:08 Reason: Trimmed most of giant necro-quote.

 2020-07-14, 19:43 #32 sweety439   Nov 2016 22·3·5·47 Posts Conjectures: * The largest double Mersenne prime is 2^127-1 * The largest Wagstaff Mersenne prime is (2^127+1)/3 * The largest Mersenne Wagstaff prime is 2^3-1 * The largest double Wagstaff prime is (2^43+1)/3 * The largest Mersenne Fermat prime is 2^17-1 * The largest Wagstaff Fermat prime is (2^17+1)/3 Also, * Phi_{Phi_n(2)}(2) is prime only for n = 2, 3, 4, 5, 6, 7, 8, 12 * Phi_{2*Phi_n(2)}(2) is prime only for n = 2, 3, 4, 5, 6, 7, 8, 10, 12, 14 Where Phi is the cyclotomic polynomial
2020-07-14, 19:49   #33
paulunderwood

Sep 2002
Database er0rr

2×3×599 Posts

Quote:
 Originally Posted by sweety439 * The largest double Mersenne prime is 2^127-1
What supporting evidence do you have to this conjecture?

Why do you believe MM127 is not prime?

In the sea of infinity what is there to stop a bigger double Mersenne prime existing?

Last fiddled with by paulunderwood on 2020-07-14 at 19:52

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