20160915, 23:01  #210 
Jul 2003
So Cal
100010010111_{2} Posts 
And 2,1019+ is done. Bruce had a fighting chance at this one!

20160918, 14:33  #211 
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
2351_{8} Posts 
Do you mean a fighting chance with ECM curves?
Bruce Dodson's limit is being 74 digits, Sam Wagstaff's limit is being 79 digits, Ryan Propper's limit is being 83 digits. 77 digits is clearly not at Bruce Dodson's limit at all! My limit  good question! 39 digits  but at IIT Madras department computing facility spent most of time cracking Cunningham tables low hanging fruits with SNFS rather than instead of ECM curves. Not even GNFS at all. Right now that I am trying it out ECM curves up on over at following four numbers (2^{8191}+1)/3, (2^{19937}+1)/3, (2^{110503}+1)/3, (2^{524287}+1)/3 with in higher bounds on a four core micro processor. And then or: Go advanced. Missing out with in some thing? There has been appearing to be no new GMPECM top 10 records results in the year 2016 tables since at least Wednesday 20 April 2016. Really? Why? Has been it is being the case that Paul Zimmermann may be that he went out Missing In Action up? Or it is being too difficult to find out one single up right now also? Or people are not being focusing up on over with in ECM curves with in right now also? And then with in ECM curves with in: And then or too: What is Joppe Bos' team being doing right now? At their own will, they could finish off with in entire Cunningham tables, Fibonacci numbers, Lucas Numbers, Homogeneous Cunningham Numbers and other twisted additive or multiplicative groups like these things. May be it is being case that NFS@Home should also to consider out factoring with in Coppersmith SNFS  Factorization Factory variant too! NFS@Home may be that it could be case also to consider out factoring with in (2^{1123}+1)/3, (3^{661}1)/2, (7^{379}1)/6, (7^{379}+1)/8 too! No nonprimitive, nontrivial factors are being known out for these Cunningham table numbers up any way at all! Not too hard to solve factoring, consider tackling also these numbers out are being up! No further more world record factorizations champions are being possibly available out any way for a while up! Why? And then or also too with in ECM curves with in: Now that the Cunningham tables have been extended to a homogeneous, i.e. uniform level such that the number of digits with in the last number entry is being balanced enough! Not like before where ever that the base 3 + and base 3  tables were being lagging behind. To calculate with extension limit × log_{10}base with in order to check out with in. 1300 × log_{10}2 = 391.34. 850 × log_{10}3 = 405.55. 550 × log_{10}5 = 384.43. 500 × log_{10}6 = 389.08. 450 × log_{10}7 = 380.29. 400 × log_{10}10 = 400.00. 350 × log_{10}11 = 364.49. 350 × log_{10}12 = 377.71. Base 6 exponent index power limit = 500. Base 7 exponent index power limit = 450. Base 8 exponent index power limit = 433 ⅓. Base 9 exponent index power limit = 425. Base 10 exponent index power limit = 400. For Fibonacci numbers, Lucas Numbers tables which share many similar properties with the Cunningham tables, Algebraic and derived factors, Aurifeuillian Factors for Lucas numbers whose exponent is a multiple of 5, Every prime factor of Fibonacci numbers and Lucas numbers always of form 2kp±1, every prime factor of Lucas numbers are always of form 1 (mod 10) or 9 (mod 10). Why? Consider with in exponent index, power growth rate α = (1+√5)/2, and β = (1√5)/2 such that Fibonacci_{n} = (α^{n}β^{n})/(αβ), and Lucas_{n} = (α^{n}+β^{n}) α, β are being roots of the equation x^{2}  x  1 = 0. Feasible Fibonacci numbers, Lucas Numbers tables limit = 2000 such that as like for the posting it that in to Mersenne Wiki web site pages: 2000 × log_{10}α = 417.98. Not like before where ever that the imbalance does occur heterogeneously do ununiformly. 1200 × log_{10}2 = 361.24. 600 × log_{10}3 = 286.27. 450 × log_{10}5 = 314.54. 400 × log_{10}6 = 311.26. 400 × log_{10}7 = 338.04. 400 × log_{10}10 = 400.00. 300 × log_{10}11 = 312.42. 300 × log_{10}12 = 323.75. Base 6 exponent index power limit = 400. Base 7 exponent index power limit = 400. Base 8 exponent index power limit = 400. Base 9 exponent index power limit = 300. Base 10 exponent index power limit = 400. Feasible Fibonacci numbers, Lucas Numbers tables limit = 1500 such that as like for the posting it that in to Mersenne Wiki web site pages: 1500 × log_{10}α = 313.48. Last fiddled with by Raman on 20160918 at 15:31 
20160919, 13:09  #212  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
best current effort; set as a limit. Any factor p70 or above is still an achievement (fewer than 25, total, so far); but I consider any p7x to be a plausible ecm target, and include smaller p8x's. Rather than setting a limit, those p79 and p83 are targets to be aimed for. There is a difference in the factors p75andup (a total of seven, exclusively due to Sam and Ryan), they're being found with limits p65/p70, even p75, only possible on large memory workstations. For contrast, my p74 was found on a commodity pc, an i7, on one of our public labs. Ryan has a post on the p75limit run; he says that he submitted 15K curves, one of which hit the p83 (as I recall). I'm up to 70K curves with B1 = 3e9, p70optimal on our old cluster, with c. 100K curves expected to find a p70. Most of those on wanted Cunninghams that Greg has shown to have no chance whatsoever of an ecm factor; say p90orup. So p77 may not be a likely target, but there is a relatively plausible fighting chance. Bruce 

20160919, 15:08  #213 
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3·419 Posts 
I meant till now. My previous (prose) post  first para graph (essay) passage  was being (especially exactly essentially) a joke. Every one can be to improving up on their own ECM curve record efforts. Please do not take it out seriously  that does up!
Okay, could NFS@Home consider finishing off with in the entire Cunningham Tables numbers by using Coppersmith SNFS? Fibonacci numbers, Lucas Numbers, Homogeneous Cunningham Numbers and other twisted additive or multiplicative groups like these things. This Factorization Factory variant is being not usable for GNFS candidates numbers, such that they need to be tackled separately! I don't think that Texas State HPC which will make out any progress up after having been holding on to this number for over six years of time period frame duration  time times know known! Some body else could claim  do tackle with in this GNFS candidate number. Ryan Propper does have got with in his own resources, so been he can surely tackle with in 2,1067+ 3,671 3,671+ apart from computation of Aliquot Sequence 4788 / 314718. Bruce Dodson can also surely tackle too 6,448+ besides of ECM curves  Lehigh University Condor Cluster. Chen + Fang + Reich + Eichhorn + Voznyy + Beschorner finished off with in 10,343 a while back! 
20160919, 23:59  #214 
Jul 2003
So Cal
3·733 Posts 
No. They report still making progress on it. It is theirs. There are plenty of others to work on.

20160921, 15:15  #215  
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3×419 Posts 
Quote:
Coppersmith SNFS  Factorization Factory variant is being suboptimal for smaller numbers  size of numbers length that ever which ever NFS@Home is being doing it that with in right now, New speed up algorithms will emerge out as we do tackle with in harder composite number candidates! Last fiddled with by Raman on 20160921 at 16:12 

20160922, 11:45  #216 
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3×419 Posts 
Every one except just a very few other people have stayed away right now from these types of factoring efforts effectively and efficiently so far.
I could have just done 10,590M c213 and 3,605+ c185 including those from extension tables at resources of IIT Madras department computing facility but I later decided to give up because: 10,590M c213 some one else would be able to sieve better and faster than me by using three large prime numbers. 3,605+ c185 from those extension tables had not been extensively done ECM curves running / executing as like the regular Cunningham tables so waste of a computational effort if a small factor lands and results. As like the regular Cunningham tables, now those from extension tables have now just been extensively done ECM curves running / executing? Every one except just a very few other people have stayed away right now from these types of factoring efforts effectively and efficiently so far. Last fiddled with by Raman on 20160922 at 11:54 
20160922, 14:39  #217 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2566_{16} Posts 

20161001, 11:23  #218 
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3×419 Posts 
But got mentally disturbed or upset and when an administrator deleted 120 million range of specialq sieved, relations accumulated for 2,2334L on Friday 4 February 2011.
May be he had been thinking that folder directories like 2_2334M, 2_1930M and 2_2334L were automated scripts or viruses. And I had to sieve again. Nevertheless I had extra time to sieve latter numbers like 10,590M and 3,605+ after wards the former numbers like 2,2334M, 2,1930M and 2,2334L were sent out for compute cluster linear algebra. At least sent out to linear algebra for some one else. 6,343 linear algebra I had been sending it out off to Tom Womack in year of March 2009. 2,985 finished off by Joppe Bos by using SNFS quickly. (May be that is Coppersmith Factorization Factory variant?) It is out off of list then! Is good to better needed to consider with for better verifying off with for factors again. As is prime factorization is not leading out to unique results away with for, different runs executing away will produce with for different results! 
20161001, 16:36  #219  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×4,787 Posts 
Quote:
And for those with cyberphobia, there is always a ream of paper and a pen (and an abacus). Take any factor that you suspect to be "wrong" and divide it using school arithmetic; it is not that hard! Quote:


20161022, 22:52  #220 
Jul 2003
So Cal
2199_{10} Posts 
2,1079+ is done.

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