20030907, 01:58  #1 
Sep 2002
296_{16} Posts 
What ( if tracked ) is the error rate for Trial Factoring
Is an error rate for Trial Factoring tracked ?
I realize that a false negative ( small factor not found/reported, when one really exists) will eventually be covered even if it takes doing a LL. What about a false positive ( small factor found/reported, when none exist) ? Is it even possible for this to happen ? Or is there some sort of very quick verification ( just do the TF calc using the factor found on the mersenne ) ? If a factor is found and no quick verification will that be the end of work on that mersenne ? Possibly missing a mersenne prime. 
20030907, 02:31  #2  
Sep 2003
5×11×47 Posts 
Re: What ( if tracked ) is the error rate for Trial Factorin
Quote:
If you have a Linux box, you can do this verification yourself. Basically, you just need to verify that 2^{p} mod f == 1 using a multipleprecision arithmetic library like GNU MP. Here p is the exponent and f is the factor. unzip factors.zip # creates the file factors.cmp decomp f 1 100000000 # creates the file factors (about 58 MB) ./factorverify factors # where the program factorverify.c is attached in a later post in this thread. # Expected output = none (no lines with false factors) On a 2.8 GHz P4 this takes less than 20 seconds for all 2.6 million factors in the GIMPS database. Edit: previously instead of using the factorverify.c program, this post used: cat factors  sed e 's/^\(.*\),\(.*\)$/(2^\11)%\2/'  xargs ./pexpr  grep n v '^0$' # Where pexpr is a small program from the demos directory of the GMP source code. # Previous line outputs linenumber of any falsepositives in the "factors" file. # Expected output = none. This was clumsier and slower. Last fiddled with by GP2 on 20031023 at 19:44 

20030907, 02:34  #3 
Aug 2002
Termonfeckin, IE
2^{2}×691 Posts 
There is backend verification so you cannot get false positives. False negatives I'm sure have happened but are probably relatively rare.

20030907, 03:12  #4 
Sep 2003
5×11×47 Posts 
Another question for those worried about missing Mersenne primes might be: have any exponents fallen through the cracks? That is, untested, untrialfactored, and unassigned.
This can be verified by combining all unique exponents from:  BAD (probably redundant, all exps in BAD should already be in LUCAS_V.TXT too)  LUCAS_V.TXT  HRF3.TXT  factors (the file produced by decomp f 1 100000000 on FACTORS.CMP)  nofactor (the file produced by decomp n 1 100000000 on NOFACTOR.CMP)  status.txt (the uptothehour file of all current assignments of Primenet)  cleared.txt (the uptothehour file of all current cleared exponents, probably entirely redundant unless you insist on catching any exponents cleared in the few days since the last database update of BAD, LUCAS_V.TXT etc. which occurs more or less weekly)  a 39line file of known Mersenne prime exponents and comparing this combined list of exponents to a file of all prime numbers less than 100,000,000. It is very easy to generate the latter file by the way... a program like sieve2310.c by John Moyer does this in a few seconds on a 2.8 GHz P4. The comparison can be done with standard Linux utilities like cut, sort, uniq, comm, sed. It turns out that there are no "missing" exponents less than 79.3 M. If we omit "nofactors" from the set of files above, we can discover if there are any exponents which have been trialfactored, but not LL tested or currently assigned by Primenet. It turns out there are indeed some, but this is easily explained as manual tests or people using nonPrimenet programs like Glucas or Mlucas on ranges that George has reserved for them. Here is the complete list of "trialfactored but notLLtested or currently assigned by Primenet" exponents less than M39. Nothing alarming here. On the other hand, if there was a "missing" exponent somewhere well behind the current leading edge of doublechecks, it would be time for conspiracy theories. :) 12495941 12808997 12809701 12809717 12822037 12822581 12822619 12822713 12823441 12824093 12827161 12827189 12827329 12827539 12827561 12827743 12827897 12827989 12828031 12829651 13110371 There are 20 "trialfactored but notLLtested or currently assigned by Primenet" exponents in the 12M range, 14 in the 13M range, 85 in the 14M range, etc. 
20030907, 05:16  #5 
Aug 2002
Termonfeckin, IE
2^{2}·691 Posts 
These are likely exponents released for manual testing by George. If they are in the nofactors database, then they have not slipped through the cracks.

20031023, 18:51  #6 
Sep 2003
5·11·47 Posts 
Attached is a C program that can be used to verify factors of Mersenne exponents. It's intended for use under Unix (and uses the GMP multipleprecision library that comes with most Linux distributions).
On a 2.8GHz Pentium 4, it verifies all 2.6 million factors in the GIMPS database in less than 20 seconds. Last fiddled with by GP2 on 20031023 at 19:24 
20031023, 22:26  #7  
"GIMFS"
Sep 2002
Oeiras, Portugal
17×89 Posts 
Quote:
The hrf3.txt file from the 21st of September has the exponent. It had expired a couple of days before. 

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