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: 999983 is candidate for M79 and for M6329 as 2*(6329)*79+1 and 2*(79)*6329+1 both equals 999983. 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
