20210126, 07:13  #232  
Aug 2020
2^{2}×5^{2} Posts 
Quote:
Fundamentally you have two methods to remove a candidate for good, TF or PRP. If one is faster on average, you have the highest average throughput when using that method exclusively. I don't see how it can be different. Quote:
Last fiddled with by bur on 20210126 at 07:16 

20210126, 08:21  #233  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2^{2}·503 Posts 
Quote:
Both methods are used in practice to weed out candidates they are better at sieving. TF for candidates with smaller factors and PRPTesting for the rest, even though one would have to be faster on acreage on the whole set than the other. 

20210126, 15:24  #234  
"Curtis"
Feb 2005
Riverside, CA
3×1,579 Posts 
Quote:
If TF is faster, use it exclusively. At some point in your TF efforts, TF is no longer faster, and PRP becomes faster. At that crossover point, use PRP exclusively. This is clearly the most efficient path, yet you wave your hands and use all sorts of words to make yourself feel better that it's not true. 

20210127, 09:43  #235  
Romulan Interpreter
Jun 2011
Thailand
9379_{10} Posts 
Quote:
By "speed of TF" we mean how fast you can eliminate an exponent, by finding a factor. TF programs seem "much faster", they do many tests in the wallclock time taken by a PRP test, but to find a factor, you need to do many assignments (roughly, equal to the bitlevel, i.e. if you look for 70 bits factors, you will need to test about 70 exponents, to find a factor). If your hardware can test 70 exponents to 70 bits faster than it takes for the same hardware to do a PRP for an exponent of the same size (plus or minus a little change, considering the certification process, error rates, vanity of having a factor as opposite of having a PRP residue, whatever rows your boat), then YOU SHOULD CERTAINLY DO ONLY TF to 70 bits. This is how GIMPS works since its inception, if we make abstraction of the people who only run TF because they want more credit, or they like to have found factors, or (I would say "selfish") people who only run LL/PRP because they want the glory of finding a prime and take George's money. Most users here will try to help the project most, by optimizing their rate of getting rid of exponents, at front wave, either doing TF or PRP. Of course, the options will wary in time, according with the exponent size at the front level and the bitlevel that has to be trialfactored, you can do PRP today because the bitlevels are very deep here, and TF next month if your exponent gets higher and the bitlevel is lower or stays the same, but once the exponent and bitlevel is given, and assuming you know your hardware, you should optimally chose ONE of them, and DO THAT ONE ONLY. Last fiddled with by LaurV on 20210127 at 09:58 

20210219, 08:30  #236 
Sep 2002
Database er0rr
111000100101_{2} Posts 
Congrats to Serge Batalov for the smallest known 1 million digit prime:
10^999999 + 308267*10^292000 + 1 Can this be limboed? 
20210219, 08:48  #237  
"Jeppe"
Jan 2016
Denmark
2·83 Posts 
Quote:


20210219, 19:36  #238  
Nov 2016
B04_{16} Posts 
Quote:


20210219, 19:42  #239 
Sep 2002
Database er0rr
7045_{8} Posts 

20210302, 18:52  #240 
Sep 2002
Database er0rr
3·17·71 Posts 
DRUG is PRP top
We had a nice email from Jeff Gilchrist this morning saying one of his computers had reported:
Code:
2^1338029827 is base 3Fermat PRP! (4027872 decimal digits) Time : 9677.550 sec. 2^1338029827 is Fermat, Lucas and Frobenius PRP! (P = 5, Q = 5, D = 5) Time : 75222.576 sec. It is official now Last fiddled with by paulunderwood on 20210305 at 05:38 
20210311, 22:52  #241 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10010010101111_{2} Posts 
A new Generalized Cullen number  4'143'644 decimal digits.

20210312, 21:01  #242  
Dec 2011
After milion nines:)
3·11·43 Posts 
Quote:


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