20180215, 16:15  #23 
"/X\(‘‘)/X\"
Jan 2013
Ͳօɾօղէօ
5342_{8} Posts 
There's nothing wrong with PHP, but it's a very incoherent language. I've been using it professionally for nine years, and a lot longer before that. It's the Visual Basic of the modern era.

20180215, 18:47  #24 
Aug 2006
13344_{8} Posts 

20180215, 21:52  #25  
"Victor de Hollander"
Aug 2011
the Netherlands
2230_{8} Posts 
Quote:
I can understand why people are reluctant to spend 0.12 GHzday to try P1 if a PRP test on these low exponents only takes 0.15 GHzday 

20180215, 23:39  #26 
Aug 2002
Buenos Aires, Argentina
2·659 Posts 
GIMPS does care about all prime factors of Mersenne numbers. That's why it stores all prime factors found (not only the first one) and on GIMPS you can select to perform ECM on numbers that have at least one factor known, and you can also perform PRP on cofactors.
Notice that with the ECM worktype (3 curves with B1=50000, B2=5M), my computer found factors for the following Mersenne numbers: M2302451, M2314951, M2333651, M2339797, M2357791, M2364161, M2365313 and M2379851 (14 days, two threads) while using P1 (B1=500000, B2=15M) my computer found factors for the following Mersenne numbers: M2300017, M2300057, M2300153, M2300563, M2300731, M2300999, M2301199, M2301251 and M2301421 (1 day, 1 thread). In both cases these numbers already had factors found. It is clear the P1 in this range can find a lot more factors than ECM. From TJAOI's work, the prime factors to be found will be greater than 34*10^{18} (about 65 bits). Last fiddled with by alpertron on 20180215 at 23:43 
20180216, 03:17  #27  
Jun 2003
1000111110001_{2} Posts 
Quote:
However, ... Now that I think about it, it might be underestimating the probability. Basically, the formula looks at the probability of k part of P=2kp+1 being B1/B2 smooth. It assumes that k is a random number. However k is not a random number. It is a factor of a (prime  1). This ought to have different probabilities of divisibility by other primes. (For example, if k is truly random, it will be divisible by 3 with probability 1/3. However, since 3 cannot divide P, it will divide P1 with probability 1/2, hence it will divide k with probability 1/2). This might mean that the formula needs to be tweaked by a correction factor. It might not matter much in the end though  the formula as such is a crude approximation. Anybody willing to work on a more sophisticated estimate? 

20180216, 16:35  #28 
Sep 2009
13·139 Posts 
Or the modern equivalent from intercal.txt.gz:
Code:
//INTERCAL PROC //COMPILE EXEC PGM=INTERCAL //STEPLIB DD DSN=U.INTERCAL.LIBRARY,DISP=SHR // DD DSN=SYS1.FORTLIB,DISP=SHR //SYSPRINT DD SYSOUT=A,DCB=(BLKSIZE=992,LRECL=137,RECFM=VBA) //SYSPUNCH DD DUMMY //SCRATCH DD DSN=&COMPSET,UNIT=SYSDA,SPACE=(CYL,(3,1)),DISP=(,PASS) //EXECUTE EXEC PGM=EXECUTE,COND=(4,LT) //SOURCES DD DSN=U.INTERCAL.SOURCES,DISP=SHR //STEPLIB DD DSN=U.INTERCAL.LIBRARY,DISP=SHR // DD DSN=SYS5.SPITLIB,DISP=SHR // DD DSN=SYS1.FORTLIB,DISP=SHR //SYSIN DD DSN=&COMPSET,DISP=(OLD,DELETE) //SYSOBJ DD SYSOUT=B,DCB=(BLKSIZE=80,LRECL=80,RECFM=F) //SYSPRINT DD SYSOUT=A,DCB=(BLKSIZE=992,LRECL=137,RECFM=VBA) //SYSPUNCH DD DUMMY // PEND 
20180216, 20:28  #29  
Banned
"Luigi"
Aug 2002
Team Italia
7^{2}×97 Posts 
Quote:


20180217, 04:43  #30 
Romulan Interpreter
Jun 2011
Thailand
8,543 Posts 
I always use to multiply that by 2, which somehow matched with my results (number of factors) in the past when I had like 20 GPUs doing TF assignments from Chris' site. You may remember that I was always finding more factors than expected, and I used to joke that I am a lucky guy (which I still do sometimes). But a real reason may be that we need to multiply everything by 2 or so, including for P1. I can not offer a more "mathematical" explanation for it, but a reason may be the fact that indeed, k in q=2kp+1 is not a random number, but it can only be "0 or 1 (mod 4)" if p=3 (mod 4), or it can be "0 or 3 (mod 4)" if p=1 (mod 4). So, it is somehow "half" of the four possible cases in each category.
For the case in this thread, the sample is too small. I also remember having long strikes of bad luck, where I could not uncover a P1 factor for weeks, and then finding lots of factors in the same day (or week). 
20180217, 17:35  #31 
Sep 2009
13·139 Posts 

20180220, 23:27  #32  
"William"
May 2003
New Haven
4466_{8} Posts 
Has anybody checked if the heuristic for B1/B2 smooth is near the real value? The comments in the code sample indicate that the code generates a smashup estimate calculated from the function for being bsmooth at multiple values of b. But there is a known formula for being B1/B2 smooth. It may be more complex than we want to calculate on the fly, but a handful of test cases could be calculated.
Here are the code comments: Quote:
I don't currently have access to good tools to do the numerical integration  perhaps someone else can check a few cases? 

20180221, 14:09  #33 
Aug 2006
16E4_{16} Posts 
I don't think Dickman's rho is particularly accurate in that range  I wonder if we'd be better off checking numbers for smoothness directly.

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