20191012, 01:23  #1 
Jun 2019
Boston, MA
46_{8} Posts 
TF small exponents on GPU?
Is there any way to do TF work on very small (ie less than 10^5) exponents using GPUs? It seems that mfaktc and mfakto have lower limits for exponents unless there is some way to modify these—is there an alternative GPU program for this type of work?

20191012, 01:44  #2 
P90 years forever!
Aug 2002
Yeehaw, FL
2^{2}·3·587 Posts 
If there is a way to do TF on small exponents I hope no one tells you.
TF on exponents below 10,000 is a complete waste of time. You will find zero factors  guaranteed. To find new factors you must do ECM. And then you'll need a lot of luck, but at least you won't be wasting your time and resources. 
20191012, 03:21  #3 
Sep 2003
2,579 Posts 
Here is the ECM Report for exponents under 10,000.
Based on this, we know with a very high degree of certainty that there are no unknown factors smaller than 30 digits for exponents in this range, or about 100 bits. And that's a very conservative estimate; actually, no factor smaller than 35 digits (116 bits) has been discovered for exponents in this range in the past eight years. Trial factoring can't find such large factors, unless you spend way more than a trillion years on it. 
20191012, 03:25  #4 
Sep 2003
2,579 Posts 
You probably will be wasting your time, because Ryan Propper is already working that range and finding large factors and he clearly has a ton of resources.

20191012, 03:58  #5 
Jul 2003
wear a mask
2·17·41 Posts 
Is there a way to perform ECM curves on a GPU?

20191012, 04:07  #6  
P90 years forever!
Aug 2002
Yeehaw, FL
1101110000100_{2} Posts 
Quote:
I think GMPECM can be compiled to run stage 1 on very small numbers, but I don't know any of the details. 

20191012, 05:35  #7  
Sep 2003
2,579 Posts 
Quote:
Quote:


20191012, 08:26  #8  
Apr 2019
5×41 Posts 
Quote:
Quote:
So the first number: M1213 for example has a composite cofactor of 986 bits. 

20191012, 12:33  #9 
Random Account
Aug 2009
U.S.A.
2×3×227 Posts 

20191012, 14:45  #10  
Sep 2003
2,579 Posts 
Quote:
I used FactorDB for the cofactor size in digits, so the bit size is approximate and the actual value may be off by one or two or three. Using https://www.mersenne.ca/manyfactors.php I made sure that there are no other candidates of any size with 5 factors or more. For any exponent above 1500 with only 4 factors or less, the factors would need to total at least 482 bits to make the list (i.e., be of size at least 120 bits on average), and that's the absolute bestcase scenario. Highly unlikely. Code:
1213 297 digits ≈ 987 bits 1217 248 digits ≈ 824 bits 1229 284 digits ≈ 944 bits 1231 329 digits 1237 303 digits ≈ 1007 bits 1249 326 digits 1259 309 digits ≈ Last fiddled with by GP2 on 20191012 at 14:56 

20191013, 03:20  #11 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
3×5×17^{2} Posts 
I suspect very slim odds.
In the past several months Ryan Propper found a first factor for about a dozen exponents under 9999.
None of the factor found results indicated how many curves were tried or at what B1/B2 levels. Nor were any unsuccessful attempts reported. But I suggest that in order to find that many factors for so many small exponents he must have done a heck of a lot of curves. Since they were not reported these curves must be redone in order to be recorded. Further I hope to be proven wrong soon, but I tend to believe that since Ryan hasn't reported any Factors recently he has done all the ECM for these small exponents that he sees value in. Maybe all the way to PrimeNets 30 or 40 or 50 + digits levels. If he did his ECM in a way that he can indicate the number of curves done at each level it could save the rest of us a lot of ECM work that has no chance of finding a factor. 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Bug in generating ECM work for small exponents  monsted  PrimeNet  6  20190928 03:25 
Sieving with powers of small primes in the Small Prime variation of the Quadratic Sieve  mickfrancis  Factoring  2  20160506 08:13 
P1 on small exponents  markr  PrimeNet  18  20090823 17:23 
256KB L2 limited to small exponents, but 8MB L3  xorbe  Information & Answers  2  20090208 05:08 
New "small" exponents available  Prime95  PrimeNet  6  20060521 15:38 