20190318, 17:54  #1 
"Luke Richards"
Jan 2018
Birmingham, UK
2^{5}·3^{2} Posts 
...merely a question about ECM world record?
A quick Google and a read of the Wikipedia page for ECM factoring list the all time record factor found by ECM at 83 decimal digits long, a 2013 record.
Is this 'fact' up to date? Does the record have to be a prime? I ask because today I used the ECM function on Prime95 to find a 106 digit long composite factor of a 240,000 digit number. 
20190318, 18:07  #2 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
3^{2}×1,277 Posts 

20190318, 18:38  #3  
∂^{2}ω=0
Sep 2002
Repรบblica de California
11743_{10} Posts 
Quote:


20190318, 19:55  #4  
"Luke Richards"
Jan 2018
Birmingham, UK
2^{5}·3^{2} Posts 
Quote:
Hi ewmayer. I'm assuming you didn't mean to come across quite so brusquely, but your tone is a little offputting here. No, I didn't. The websites I saw which list the records give no indication of a requirement for the factors to be prime, nor to have been previously undiscovered. They merely state that they are showing the largest factors found using ECM methods. After all, the algorithm does not know that the factors are in a table of known factors. But I think what was clear from the replies of others, is that there was (as I suspected) more to it than just finding a factor, rendering this quite unwelcoming and accusatory response somewhat unnecessary. 

20190318, 21:31  #5 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3·3,313 Posts 
Many people have found very large composite factors with ECM.
It is very easy to construct an input such that the ECM factor will be enormous (>>106 digits). 
20190318, 21:56  #6 
∂^{2}ω=0
Sep 2002
Repรบblica de California
11,743 Posts 
Didn't mean to offput anyone, just pressed for time and "understanding the occurrence of composite factors is a really basic part of using such factoring algorithms". If you want to claim a record in the 100m sprint, you surely understand you don't start the race from the 90m mark. If saying so makes me 'brusque', so be it.

20190318, 22:01  #7  
"Luke Richards"
Jan 2018
Birmingham, UK
2^{5}·3^{2} Posts 
Quote:
Clue is in the name really... "100m sprint" So really "largest factor found by ECM" should be called "largest undiscovered prime factor found by ECM". Otherwise its akin to calling it "First person to cross the finish line" rather than "100m sprint". 

20190318, 22:44  #8 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
1101010110101_{2} Posts 
Communication is hard.
What A means> what A says or writes > What B hears or reads > What B interprets it to mean. Most of inperson communicatioin is nonverbal. Here, there's no smile or nod or other gesture to show that A means it in a friendly helpful way. If B was excited about something, then disappointed, it's easy to perceive negativity where none's meant or perhaps where none's objectively present. Closing the loop helps. B states his interpretation. A responds, not exactly what I meant; (clarification follows). Different styles/cultures can complicate it. On another note, 106 digits is around 352 bits. Larger composite factors are known. Consider an assortment of partially factored Mersenne numbers with several prime factors, totaling 400650 bits per number. https://www.mersenne.ca/manyfactors.php Factoring for GIMPS sometimes produces composite factors. The Primenet server checks the reported factors for whether they are composite, and whether they are actual factors of the Mersenne number; errors do occur. A list of prime factors is much more succinct than a list of the prime factors plus all composite combinations of them. Last fiddled with by kriesel on 20190318 at 22:46 
20190318, 22:56  #9 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
7×23×41 Posts 

20190319, 09:13  #10  
Mar 2018
81_{16} Posts 
lukerichards,
Quote:
Last fiddled with by DukeBG on 20190319 at 09:19 

20190319, 16:27  #11  
Feb 2017
Nowhere
2·3·997 Posts 
Quote:
Before siccing ECM onto a number, it's prudent to make sure there are no small factors. With numbers of the form a^n  1, a first whack is to bust it up into cyclotomic factors. Then, Aurefeuillian and intrinsic factors are lowhanging fruit. Then, you can strip out any small factors. Just by way of practice, I did this with 2^5040  1. There weren't many composites left standing. They were all factors of the larger "primitive parts" (cyclotomic factors, with any intrinsic prime factor divided out). Of course, with a = 2 and other small bases, this work (and a great deal more besides) has already been done. The remaining composites are listed in tables. Those would be your quarry for hunting with heavy artillery. 

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