20070724, 21:57  #1 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
2·3^{2}·277 Posts 
Can anyone explain 'iterations' for factoring?
We typically see numbers between 1 and 16 under iterations for factoring; however there is the odd exception where the number of iterations is significantly higher:
For example: 43163371 F 63 10 1.5 0.8 60.8 23Jul07 09:13 22Jul07 03:33 jamamastaha Rusada65 43159609 F 63 10851596 1.7 0.3 60.3 22Jul07 22:42 21Jul07 22:42 Team_Bundu GordonVista Last fiddled with by petrw1 on 20070724 at 21:58 
20070730, 19:45  #2 
Jul 2007
Poland
233_{8} Posts 
16 series, 16 iterations
Numbers 1..16 are can be explained if George W. still uses his trick: there are 16 numbers between 0 and 120=2^3*3*5 mutually prime with 3,5 and equal +/1 mod 8: 1,7,17,23, 31,41,47,49, 71,73,79,89, 97,103,113,119. Possible divisors (in a form 2kp+1) belong to one of these 16 series and the numbers you ask indicate them, I think.
I have completely no idea on 10851596. 
20070731, 05:01  #3  
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
2×3^{2}×277 Posts 
Quote:


20070731, 08:17  #4  
"Mark"
Feb 2003
Sydney
3·191 Posts 
Quote:
43159609 is interesting... that status data is probably showing it being LL tested, but only TFd to 63 bits. The latest GIMPS nofactor data, from about the same time as the OP, has it TFd to 67 bits  better but not good enough. It ought to be done to 68 bits. This might explain why it's now not in either cleared.txt or status.txt (dated 31 Jul 2007 07:00 UTC). It's probably available for the last bit of TF, despite having completed LL testing. 

20070731, 08:57  #5  
Jul 2007
Poland
5·31 Posts 
Quote:
Each range (to 63, 64, and so on) is proceeded from 1 to 16. At least it was when I was more interested in algorithms and methods used by George. If you use Manual Communications just before and just after switch from 2^b to 2^(b+1) you can see (in your individual report at the PrimeNet) that iteration number has dropped from, say, 15 to 2. 

20070731, 09:18  #6 
Jul 2007
Poland
5×31 Posts 
PS
It is why Prime95/mprime does not determine the smallest factor as a rule. After finding a factor = 47 mod 120, e.g., it does not work on further possiblities (49, 71, ... mod 120). Remember that GIMPS means "Mersenne Prime Search". This project organized by G. Woltman does not bother with factoring composite Mersenne numbers, but some other projects do.

20070731, 16:04  #7 
Mar 2007
B3_{16} Posts 
From my experience, the 1  16 method was used in version 24 and prior. It would cycle through 1 through 16 for each bit level. Version 25 now shows the progress at each bit level in a manner similar to the progress of LL tests. That is in absolute numbers up to the the value of M being tested.

20070810, 23:47  #8 
Jul 2004
Mid Calder, Scotland
5×37 Posts 

20070811, 18:28  #9 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
137A_{16} Posts 
Well this does support "monst" suggestions that V25 shows iterations differently ... not 116 but rather 1  P.

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