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Old 2010-03-20, 18:01   #1
MatWur-S530113
 
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Default Exponents which don't need any more ECM

Hello,

I recognized that there are some users, who run ECM curves on M-numbers, 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 text-file with the prp-tested exponents.

regards,

Matthias
Attached Files
File Type: txt results_prp-65537.txt (2.4 KB, 193 views)
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Old 2010-03-20, 18:49   #2
R. Gerbicz
 
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Quote:
Originally Posted by MatWur-S530113 View Post
Hello,

I recognized that there are some users, who run ECM curves on M-numbers, which have a last remaining cofactor, which is prp.
Actually some of them are proven primes, see: http://primes.utm.edu/top20/page.php?id=49

Some of them is proven in 2002! It is interesting that gimps is doing ecm works on primes.
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Old 2010-03-20, 19:30   #3
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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 prp-tests, 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 ECM-list).

regards,

Matthias
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Old 2010-03-20, 20:35   #4
Prime95
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Quote:
Originally Posted by MatWur-S530113 View Post
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.
Done
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Old 2010-03-20, 20:39   #5
Prime95
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Quote:
Originally Posted by MatWur-S530113 View Post
My real problem is, that I made a few thousand prp-tests, 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 ECM-list).
Something like that is on the to-do list. The client is already set up to receive PRP tests and send in PRP results (as you've seen). The server is not yet ready to hand out PRP assignments and process the results.

I'd probably keep track of all exponents below 10 million to see which ones are fully factored.
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Old 2010-03-20, 20:39   #6
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Thank You
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Old 2010-03-25, 10:31   #7
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Quote:
Originally Posted by MatWur-S530113 View Post
Hello,

I recognized that there are some users, who run ECM curves on M-numbers, 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 text-file with the prp-tested exponents.

regards,

Matthias

Maybe you should add these prp's to Henri & Renaud Lifchitz's list...

See http://www.primenumbers.net/prptop/s...&action=Search
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Old 2010-03-29, 13:30   #8
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Ohh, That PRPs are already submitted (Only 10000 digits or more are allowed).
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Old 2016-10-12, 08:00   #9
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Quote:
Originally Posted by Prime95 View Post
Done
This is an old thread, but there are a few other fully-factored 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 probably-fully-factored 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 fully-factored and probably-fully-factored exponents, which are listed at http://www.mersenne.ca/prp.php . All of these exponents up to and including 63703 are proven fully-factored, while the higher ones are only probably-fully-factored.

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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