20160926, 10:00  #1 
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3×419 Posts 
Prime95  suggest using B2 bound = GMPECM default and other questions
Prime95  suggest using B2 bound = GMPECM default and other opinions
Since Monday 15 February 2016 I have been using Prime95 to extract ECM factors from large Mersenne composite numbers, and I have found out 75 so far (and counting)... Honestly, this ECM on small Mersenne composite numbers is the only work that could probably produce useful results with little amount of effort is being needed without wasting out any computing power... ECM on numbers like 2^{1277}1, 2^{1619}1, 2^{1753}1, 2^{2137}1, 2^{2267}1, 2^{2273}1, 2^{2357}1, 2^{2377}1, 2^{2423}1, 2^{2477}1, 2^{2521}1, 2^{2557}1, 2^{2671}1, 2^{2713}1, 2^{2719}1, 2^{2851}1, 2^{3049}1, etc. will probably be totally futile without producing any useful results. On the other hand, the regular Cunningham tables have been thoroughly ran away / executed away with the ECM curves by using other people  be being! Any way completely factoring the Mersenne composite numbers that I am running ECM curves on will take ages unless integer factorization is in P or advances in computing power have been made or quantum computers have been developed and implemented or advances in integer factorization algorithms have been made. Here are the 75 (and counting) factors that I have extracted from large Mersenne composite numbers.
So, roughly 280 ECM curves per factor at 25 digit level with B1 = 50000 and B2 = 5000000 and roughly 4700 ECM curves per factor at 35 digit level with B1 = 1000000 and B2 = 100000000. Does PrimeNet server assign exponents range for Prime95 for ECM curves of small Mersenne composite numbers based up on the amount of memory allocated? I initially allocated most of the machines with memory = 128 MB, some with 256 MB, a few with 512 MB and 1024 MB. My own system with memory = 64 MB. But, one of the machines allocated with 1024 MB had reset to 8 MB and later it found out its own range level of factors of 2^{130547}1 has a factor: 740710078242573288550675295986147001 and then 2^{158209}1 has a factor: 26496805856040782582748460014520511 or some 4772 ECM curves later. 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? 
20160926, 10:01  #2 
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3×419 Posts 
I would like to give a few of my suggestions to make GIMPS Project better.
Last fiddled with by Raman on 20160926 at 10:57 Reason: Added up on to point number 10 only certainly with in  last but not the least  last but not the least! 
20160926, 10:02  #3 
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
1257_{10} Posts 
Last fiddled with by Raman on 20160926 at 11:01 Reason: Reason For Editing. 
20160926, 10:03  #4 
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3×419 Posts 
Of these stuff, different things belong to different parts of this mersenne forum, nevertheless for pondering thoughts right now, placing all of them over a some, one single part of this mersenne forum piece over here by  combined thread post  where by.
I think so.
Last fiddled with by Raman on 20160926 at 11:00 Reason: Optional. 
20160926, 10:04  #5 
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
2351_{8} Posts 
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!
Factordb.com web site page does not accept with in a some of larger factors for ≥ 10000000 digits  exists out  for only of certainly! Factordb.com web site page 10000000 digit limit exists out  parallel execution queries limit exists out  sequential input queries limit exists out! Factordb.com web site page does not mark out larger known found out prime numbers and then or probable prime numbers called as out  known as out! Been got out  seeking out  looking out  obtaining out  attaining out! With in this following PARI/GP command only certainly and then or script you could be able on to getting away with the very much all most all prime factors of 2^{p}1 and then or (2^{p}+1)/3 both simultaneously  a some  of just the following given fixed form! And then or  called as out  known as out  namely  that which it that! p = (2^{79}+1)/3 Code:
p=(2^79+1)/3 forstep(q=2*p+1,10^50,2*p,if(Mod(4,q)^p==1,print(q))) Of for of for  with in only certainly  away up out down off my own  that ever which ever a way a way ever  by using be being that way  that which it that. And then or  and then or  of for from front frontier  right now that by right now that itself at this very moment variably. Very much all most all  away up out down off my own  that ever which ever a way a way ever  by using be being that way  that which it that. Once written out  one single time  time period frame duration  time times know known. A some  a some  a some  a some  a some  a some  a some  very much all most all. Away up out down off my own  that ever which ever a way a way ever  by using be being that way  that which it that. Once written out  one single time  time period frame duration  time times know known. Called as out  known as out! Once written out  one single time  time period frame duration  time times know known. And then or. Namely  that which it that. A some  a some  a some  a some  a some  a some  a some  very much all most all. Just an other point always  called as out  known as out  a some  very much all most all. A some  limit range bound level  rate ratio scale proportion  exists out  very much all most all! Double Mersenne Code:
2^{3}1 is prime. 2^{7}1 is prime. 2^{31}1 is prime. 2^{127}1 is prime. 2^{8191}1 has the factors: 338193759479, 210206826754181103207028761697008013415622289. 2^{131071}1 has the factors: 231733529, 64296354767. 2^{524287}1 has the factors: 62914441, 5746991873407, 2106734551102073202633922471, 824271579602877114508714150039, 65997004087015989956123720407169. 2^{2147483647}1 has the factors: 295257526626031, 87054709261955177, 242557615644693265201, 178021379228511215367151. Code:
(2^{3}+1)/3 is prime. (2^{7}+1)/3 is prime. (2^{31}+1)/3 is prime. (2^{127}+1)/3 is prime. (2^{8191}+1)/3 is composite. (2^{131071}+1)/3 has a factor: 2883563. (2^{524287}+1)/3 is composite. (2^{2305843009213693951}+1)/3 has a factor: 1328165573307087715777. What is being the probability and then or likelihood that at least one of the four numbers, namely  that which it that  2^{2305843009213693951}1, then, 2^{618970019642690137449562111}1, or, 2^{162259276829213363391578010288127}1, and, 2^{170141183460469231731687303715884105727}1,  could be that  must be that  ought on to be that  a some prime number? Once written out  one single time  time period frame duration  time times know known Namely  that which it that If the new Mersenne conjecture of of just that is being true, and then or (2^{2147483647}+1)/3  is being that  should be that  a some composite number  indeed obviously rather than instead of! If the new Mersenne conjecture of of just that is being true, and then or 2^{768614336404564651}1  is being that  should be that  a some composite number  indeed obviously rather than instead of! What is being the probability and then or likelihood that at least one of the four numbers, namely  that which it that  (2^{2147483647}+1)/3, then, (2^{618970019642690137449562111}+1)/3, or, (2^{162259276829213363391578010288127}+1)/3, and, (2^{170141183460469231731687303715884105727}+1)/3,  could be that  must be that  ought on to be that  a some prime number? What is being the probability and then or likelihood that at least one of the four numbers, namely  that which it that  2^{56713727820156410577229101238628035243}1, then, (2^{56713727820156410577229101238628035243}+1)/3, or, 2^{170141183460469231731687303715884105727}1, and, (2^{170141183460469231731687303715884105727}+1)/3,  could be that  must be that  ought on to be that  a some prime number? What is being the probability and then or likelihood that at least one of the four numbers, namely  that which it that  2^{715827883}1, then, 2^{2932031007403}1, or, 2^{768614336404564651}1, and, 2^{845100400152152934331135470251}1,  could be that  must be that  ought on to be that  a some prime number? What is being the probability and then or likelihood that at least one of the four numbers, namely  that which it that  (2^{715827883}+1)/3, then, (2^{2932031007403}+1)/3, or, (2^{845100400152152934331135470251}+1)/3, and, (2^{56713727820156410577229101238628035243}+1)/3,  could be that  must be that  ought on to be that  a some prime number? Mersenne Wagstaff Code:
2^{3}1 is prime. 2^{11}1 = 23 × 89. 2^{43}1 = 431 × 9719 × 2099863. 2^{683}1 = 1367 × 434836499112609694795723958417048861299768144283442662402095922180462812746769 × 67513796971703570854592232797421324116119881147340327278928245456644619398078155616494185719845536064262986241999463764460809. 2^{2731}1 has the factors: 93968249, 5235895818143, 697275709026751, 563358792984278565516774152727223543227673. 2^{43691}1 has the factors: 87383, 1398113, 4690767254460090160943, 1787363373488812416764791. 2^{174763}1 is composite. 2^{2796203}1 has the factors: 5592407, 17017419583182311, 23349981773942355169801. 2^{201487636602438195784363}1 has a factor: 14549422239062062117588852231. Code:
(2^{3}+1)/3 is prime. (2^{11}+1)/3 is prime. (2^{43}+1)/3 is prime. (2^{683}+1)/3 = 1676083 × 26955961001 × 296084343545863760516699753733387652635366098889116410731661924253563729059085336779932810899819313612925255002666691226800507277398580985624625950496168983999760414855301693388419156899841. (2^{2731}+1)/3 has the factors: 67399191280564009798331, 2252735939855296339250682011. (2^{43691}+1)/3 has a factor: 349529. (2^{174763}+1)/3 has a factor: 173085275201. (2^{2796203}+1)/3 has a factor: 129469791307. (2^{768614336404564651}+1)/3 has a factor: 3290547117383710719111443. (2^{201487636602438195784363}+1)/3 has the factors: 183756724581423634555339057, 101874969893105185923314913883. Code:
2^{3}1 is prime. 2^{5}1 is prime. 2^{17}1 is prime. 2^{257}1 = 535006138814359 × 1155685395246619182673033 × 374550598501810936581776630096313181393. 2^{65537}1 has the factors: 513668017883326358119, 883852340565787164089923172087. Code:
(2^{3}+1)/3 is prime. (2^{5}+1)/3 is prime. (2^{17}+1)/3 is prime. (2^{257}+1)/3 = 37239639534523 × 518144156602508243009 × 4000659204579114753312310878847043394855313. (2^{65537}+1)/3 has a factor: 13091975735977. Code:
Larger candidate numbers  fewer prime factors  pumped out  not  not  smaller  not  not  several  very much all most all  a some  and prime then composite or unique! Shorter candidate numbers  many prime factors  pumped out  not  not  bigger  not  not  lesser  very much all most all  a some  and prime then composite or unique! Cunningham Tables numbers candidates! Fibonacci numbers, Lucas Numbers, Homogeneous Cunningham Numbers and other twisted additive or multiplicative groups like these things. As ≠ like last final ultimate next previous letter character alphabet digit number numeral cardinal ordinal stuff. As ≠ like last final ultimate next previous letter character alphabet digit number numeral cardinal ordinal stuff. Fibonacci numbers, Lucas Numbers, Homogeneous Cunningham Numbers and other twisted additive or multiplicative groups like these things. Cunningham Tables numbers candidates! Lower candidate numbers  a lot of prime factors  pumped out  not  not  greater  not  not  sparser  very much all most all  a some  and prime then composite or unique! Huger candidate numbers  rarer prime factors  pumped out  not  not  tinier  not  not  a plenty of  very much all most all  a some  and prime then composite or unique! Last fiddled with by Raman on 20160926 at 10:35 Reason: Wrapped code tags to keep width of window in check. 
20160926, 10:16  #6  
Bamboozled!
"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across
2·7^{2}·109 Posts 
Quote:
If Prime95 used higher B2 bounds it would have to use either prohibitively large amounts of memory or much more computation in the second stage than it now does. In the latter case, relatively straightforward analysis shows that the computational costs of the increaded B2 bound greatly outweighs those incurred in running more curves at a lower B2 bound. Summary: it is not a serious issue which needs fixing immediately. It is something which has already been given careful thought. 

20160926, 11:29  #7  
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3·419 Posts 
One hour after wards posting, post edit timer expired, 76^{th} result.
76. 2^{1400251}1 has a factor: 2190658775806151479217. Entered all computational results, prime factors up in to with in factordb.com web site page only certainly. Some Prime Net assignments carry up on to 1 ECM curve with in running away only certainly  when assigned 3 ECM curves executing away. Personal computer raw draft preparation, mersenne forum appeared thread posts up on to keep with in synchronization only certainly! Quote:
Wait waitist out before ≠ after up posting thread ≠ post. Last fiddled with by Raman on 20160926 at 11:54 Reason: Reason For Editing: None, No reason was specified, (Un)title(d), Go Advanced. 

20160926, 12:09  #8  
Sep 2003
2·5·7·37 Posts 
Quote:
However the full ECM history for M1061 indicates that no ECM tests have been reported for this exponent after August 2012 (i.e., nothing beyond whatever stragglers were already in progress at the time the factor was found). So it probably wouldn't make much practical difference. Quote:
However, M1409 was only fully factored in February of this year, and the ECM history shows no further ECM tests have been done since then. Still, for the sake of consistency it should omit all the fullyfactored exponents and not just some or most of the small ones. The problem is that only mersenne.ca records information about fullyfactored and probablyfullyfactored exponents (there are 304 of them known so far) while Primenet (mersenne.org) doesn't store that information at all. Quote:
Quote:
The σ value does get reported in the results line that is sent to Primenet, so if absolutely necessary Madpoo could probably dig it out of some log file. Quote:
Quote:
P−1 testing is particularly efficient for testing Mersenne exponents because in effect the "minus 1" is cancelled out by the "plus one" of 2kp + 1. I don't think P+1 has any particular advantage for Mersenne exponents and in any case mprime doesn't implement it. Although GMPECM implements P+1 testing, it is not specifically tuned for testing Mersenne numbers quickly. I wonder if anyone has ever used P+1 testing successfully to find a factor of a Mersenne number (apart from maybe very small exponents). 

20160926, 13:16  #9  
Sep 2003
2590_{10} Posts 
Quote:
However, this is just for fun. It doesn't really align with the goals of the project. For exponents that have been LL tested composite but have no known factors, it is still useful for the project's goals to look for a (first) factor, for two reasons. First of all, there are a bunch of older machines which lack the horsepower to do anything else, but they can still run a few ECM curves. This keeps users involved who might otherwise be unable to participate, and who knows, someday they might get a new fast computer. Second, it is qualitatively much better to possess a factor than just an LL test. If someone supplies you with a factor, it is trivial to verify it for yourself. It takes only a few microseconds of computing time, in fact you can verify the entire database of tens of millions of factors in one shot, in a minute or two. On the other hand, if someone only supplies you with an LL residue, then it is much more laborious to verify it for yourself. The time to run an LL test on M_{p} is O(p^{2} log p). So in the meantime you have to worry whether the user is reliable (was the test faked?), whether the software is reliable (does it have rare bugs?), and whether the hardware is reliable (are there memory errors?). So long as there are Mersenne exponents with no known factors, those will always be higher priority for the project's goals than Mersenne exponents that already have known factors. 

20160926, 13:34  #10 
Sep 2003
5036_{8} Posts 

20160926, 15:03  #11 
Bamboozled!
"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across
2×7^{2}×109 Posts 

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