20100320, 18:01  #1 
Apr 2007
Spessart/Germany
2·3^{4} Posts 
Exponents which don't need any more ECM
Hello,
I recognized that there are some users, who run ECM curves on Mnumbers, which have a last remaining cofactor, which is prp. The following exponents can be put out of the list 'ECM with known Factors': 6199, 6337, 10007, 10169, 11813, 17029, 17683, 20887, 26903, 28759, 28771, 29473, 32531, 41263, 57131, 58199, 63703. I checked all exponents up to 65537. I attache a textfile with the prptested exponents. regards, Matthias 
20100320, 18:49  #2  
"Robert Gerbicz"
Oct 2005
Hungary
2^{2}×367 Posts 
Quote:
Some of them is proven in 2002! It is interesting that gimps is doing ecm works on primes. 

20100320, 19:30  #3 
Apr 2007
Spessart/Germany
242_{8} Posts 
yes, on Chris Caldwell's prime pages some of the remaining cofactors are listed as proven primes. But it must be an older problem. A few days ago I found a factor of M10211 with a remaining prp (and I proved it prime with primo), but this number is already put out of the ECM list. The same with the low exponents 887, 941, 1013, 1087, 1181 and 1187 which are done by GNFS or ECM by the playstation team this year, they are already out of the list. My real problem is, that I made a few thousand prptests, then prime95 posted a few thousand results and I got a few thousand answers:
PrimeNet error 45: Invalid result type ar: invalid result type: 150 imho the server needs a subroutine to check at least the results, which say that a cofactor is prp (and after checking the result, the server should delete the number from the ECMlist). regards, Matthias 
20100320, 20:35  #4 
P90 years forever!
Aug 2002
Yeehaw, FL
2^{2}·1,873 Posts 

20100320, 20:39  #5  
P90 years forever!
Aug 2002
Yeehaw, FL
2^{2}·1,873 Posts 
Quote:
I'd probably keep track of all exponents below 10 million to see which ones are fully factored. 

20100320, 20:39  #6 
Apr 2007
Spessart/Germany
2·3^{4} Posts 
Thank You

20100325, 10:31  #7  
Mar 2010
On front of my laptop
7·17 Posts 
Quote:
Maybe you should add these prp's to Henri & Renaud Lifchitz's list... See http://www.primenumbers.net/prptop/s...&action=Search 

20100329, 13:30  #8 
Mar 2010
On front of my laptop
7·17 Posts 
Ohh, That PRPs are already submitted (Only 10000 digits or more are allowed).

20161012, 08:00  #9 
Sep 2003
2×5×7×37 Posts 
This is an old thread, but there are a few other fullyfactored exponents now that could be removed from the ECM report, since they don't need any further testing: 1409 2087 2243 2381 10169 57131 58199 63703
In addition, there are a number of probablyfullyfactored exponents, namely 82939 and higher, which no one in their right mind would do any further ECM testing on, even though the final cofactor is too impracticably large for a formal primality proof. It appears that most of these are still in the ECM report, although 87691 seems to have been removed already. There are 305 fullyfactored and probablyfullyfactored exponents, which are listed at http://www.mersenne.ca/prp.php . All of these exponents up to and including 63703 are proven fullyfactored, while the higher ones are only probablyfullyfactored. In addition to removing these from the ECM report, perhaps the "Current Progress" menu at mersenne.org could incorporate an item for "Fully Factored or PRP" underneath the "Known Primes" item. This information is part of the Mersenne knowledge base after all. 
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