SV: Mersenne: Factors aren't just factors
reaction to another mail about this This happens all the time in different shapes so I would expect some happy day we found a crosslinked factor. we will never find a factor who is a factor of Mx and also of My simply because every factor give only one count with my algoritm and is factor of one or zero mersenne numbers for example the factor 7 is a factor of 2^3-1 and 2^6-1 and 2^9-1 and 2^12-1 etc.. but only 2^3-1 of a mersenne number so a factor can never be factor of Mx and My both Yep, you're so truly right. After I used the reverse factoring algorithm a bit harder it is not difficult to see that when you arrive at 1 (and started at 1) the same pattern will repeat (after all we are multiplying by 2 and mod'ing the same value repeatedly from 1). Some how it is no longer a mystery that 13421 is a factor of any 2k*61 (2684 in this case) as 61 is the highest prime in the factorized values of 13420 (factors: 2*2*5*11*61). Again: 2*5*11 is only the k. And also I have found reverse factoring will find it self as a value for Mprimes, 31 is a factor of M5 and so is 127 a factor of M7, and most often just it self -1 for very uinteresting values, like 107 divides M106. :-( On the other hand this insight could make me/us construct interesting and primetested values beyond the scope of Mprime (eg. max 66 bits for numbers below 21.600.000) but in the scope of GIMPS (any prime apx.72.300.000). At least I got one machine for which mprime has no relevance as some uncontrolled reboots happens and I would like a sleep to occur every 10 seconds. Then I can write my own reverse facoring for this machine - it is on anyway for other purposes. Happy hunting tsc _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
SV: Mersenne: Factors aren't just factors
M89 is prime! M89 = 618.970.019.642.690.137.449.562.111 with no known factors. So it would be lovely if we could rule out any possible Mx if x had earlier been a factor for any other My. :-) But no. M11 proves this so nicely: M23 has factors, M89 none. I've started looking for some factors, where f is both factor of Mx and of My. The chance is there as Mx calls for factors of the form 2kx+1 and My calls for 2Ky+1. Let's have an example: 547 is candidate for M7 as for M13: 2*(3*13)*7+1 and 2*(7*3)*13+1 or better: 83 is candidate for M79 and for M6329 as 2*(6329)*79+1 and 2*(79)*6329+1 both equals 83. This happens all the time in different shapes so I would expect some happy day we found a crosslinked factor. happy hunting tsc Torben, I noticed something along those lines long ago: the first non-prime Mersenne number is M11 which factors to 23 times 89. The very next non-prime Mersenne number is M23, and M89 is also not prime. It occurred to me then that possibly Mx is never prime if x is a factor of a Mersenne number, but it was just an observation and I never got around to pursuing it. If so, then it would (although only very slightly) reduce the number of candidates to be tested. So I am just as curious as are you. _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
