Torben Schl�ntz wrote: > > I'd also like to know about any number fully factorized, whatever size > it might be, and whatever size the factor(s) might be.
Try Will Edgingtons's page, http://www.garlic.com/~wedgingt/mersenne.html . Use used to keep a comprehensive archive of known Mersenne factors. I am not sure how up to date this files are, but it is a good starting point. > Besides I have the question: "why does the advanced facor algortithm of > prime95 somtimes find 2 factors"? This happens eg. at M1289, has > 108817410937 and 15856636079 as factors? I'm not quite sure which advanced factor algorithm you mean. There are two possibilities: P-1/ECM: These find all factors that have the required property, i.e. that the starting element in the group has a group order whose factors are only primes and prime powers <=B1, and at most one prime <=B2. It is perfectly possible to find several factors in one run, or even all factors, in which case the algorithm outputs the input number. Trial factoring: Trial factoring proceeds by trying candidate factors to see if they divide your input number. One normally tests a candidate factor f only after having tried all candidates <f (or at least <sqrt(f)), so that the candidates can be restricted to primes. For if d|f, d|the input number and should have been found before f. Restricting the f's to only primes is too expensive, so one strikes a balance by excluding only those f which have factors smaller than some limit, in a process called sieving. The optimal sieving limit depends on how fast the sieving can be performed, and how long it takes to test one surviving candidate. Thus, a composite factor can be found if all it's prime factors are above the sieving limit. I do not know what the current sieving limits in Prime95 are, but they surely are <15856636079 for all trial factoring depths. It would be rather easy to test factors for primality once they are found and not print them or comment them as not prime when printed. However, the main purpose of trial factoring in Prime95 is to find smallest factors to eliminate Mersenne prime candidates, here such a test is not neccessary as the smallest factor of a number is always prime. Alex _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
