20160618, 21:39  #34  
I moo ablest echo power!
May 2013
11011111000_{2} Posts 
Quote:


20160619, 09:43  #35  
Jun 2003
1010000011111_{2} Posts 
Quote:


20160619, 11:07  #36  
Romulan Interpreter
"name field"
Jun 2011
Thailand
9,787 Posts 
Quote:
On your particular C124 example, Yafu gets out small composites and a PRP9, leaving a C109 in few seconds, which survives the 0.33 ECM, therefore the time to factor it will be the time to run GNFS on a C109. In 4cores, 3.8GHz machine where I tried it, ECM is about 24 minutes, poly search about 1213 minutes, sieving about 90 minutes to 2 hours depending of how a good a poly you got, then the LA and square root up to a hour depending on your luck with the square root. You can't make it faster, with this hardware. 

20160619, 11:27  #37 
"James Heinrich"
May 2004
exNorthern Ontario
2^{4}·3·73 Posts 
I don't remember which exponent it's from offhand. These numbers will either kvalues of factors, which could either be factors as found (either prime or composite factors), but mersenne.ca also displays kvalues of all composite factors of all known prime factors as well, which is probably what my example is.

20160619, 11:30  #38  
Romulan Interpreter
"name field"
Jun 2011
Thailand
263B_{16} Posts 
Quote:
(edit: here is how I found it: Code:
gp > p=2; x=0; until(x==p, a=0; until(a,[p=nextprime(p+1), a=isprime(b=2*k*p+1)]); print(p": "x=getp(b,p+1))) 331: 332 379: 380 1171: 1171 gp > ## *** last result computed in 1,382 ms. gp > Code:
/*get smallest p such as n divides 2^p1*/\ /*print(k++", "ggg=2*k*(1<<311)+1", "gggg=getp(ggg,10^10)", "ggg%gggg", "isprime(ggg))*/ getp(n,limt)= { if(n<3  n%2==0, print("Only odd positive numbers!");return); rg=1; sm=0; until(rg==1  sm>=limt, rg+=n; while(rg%2==0 && sm<limt, rg>>=1; sm++; if(bitand(sm,1048575)==0, printf("...%d...%c",sm,13)); ) ); return(sm); } edit 3: just realized I didn't give the factors, in case your tool still crunching: P65 = 79001680667399413021755551127728881024073264821649477463074552981 P44 = 80372772078870023311028629526527251806209541 NFS elapsed time = 8766.1264 seconds. Last fiddled with by LaurV on 20160619 at 11:44 

20160619, 13:04  #39  
Jun 2003
3·17·101 Posts 
Indeed, I should've known that this would've come out of a big NFS factor of a small mersenne.
Quote:


20160619, 13:07  #40  
Romulan Interpreter
"name field"
Jun 2011
Thailand
9,787 Posts 
Quote:
Which is ok, even if they are meaningless. (edit: the "too big" in this case is a very good thing too, they don't need to waste cpu time for factoring) Last fiddled with by LaurV on 20160619 at 13:08 

20160619, 13:40  #41 
"James Heinrich"
May 2004
exNorthern Ontario
2^{4}×3×73 Posts 

20160619, 14:29  #42  
Jun 2003
3·17·101 Posts 
Quote:
PS: I am also unsure of the usefulness of the TF GHz days displayed against composite factors, because it doesn't correspond to the actual way in which TF would discover those factors. 

20160619, 19:04  #43 
Sep 2003
5·11·47 Posts 
It's redundant to store both the factor and the kvalue in the database, since one is so easily derived from the other, via f = 2kp + 1.
But arguably it's k that we should store and keep track of, and not the full factor. The factor itself is relatively uninteresting, in the same way that the actual decimal expansion of a Mersenne number is uninteresting, as opposed to the exponent. At the moment 28,869,906 factors are known, for p between 0M and 1000M. Since p is on average a bit less than 9 decimal digits, that means just under 259MB (247 MiB) of wasted storage, since the factors are stored as strings. Since the distribution of k skews overwhelmingly toward small values, the savings would be even greater percentagewise. In the vast majority of cases, we could replace a 9 or 10 digit factor with a one or two digit k value. On the other hand, one advantage of storing the factor itself is that mathematically any given number can be a factor of at most one Mersenne number with a prime exponent (i.e., the exponents that we care about). So you can make the factor field the primary index of your database table. But presumably it would be just as efficient to use (exponent, k) as a unique index. Last fiddled with by GP2 on 20160619 at 19:20 
20160619, 19:18  #44  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
Quote:
Last fiddled with by science_man_88 on 20160619 at 19:19 

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