help wanted: "Mersenne-Base Cunningham numbers"
help wanted: "Mersenne-Base Cunningham numbers"
I am looking for help to get factorizations of "Mersenne-Base Cunningham numbers" that is M^k-1 where M is usually the ninth Mersenne number 2^61-1 .
Such factorizations are necessary to find primitive polinomials of order k in the prime base M. This means that there are many problems in applied math that can benefit from this.
At this point many smallish k have been done, I am currently looking to finish k=120 but also some others if indeed help is on the way.
For k=120 there is only one factor remaining but it is a hard one c281, at the moment ECM with approx thousand curves at 260E6 have been run.
<c281> is
29921110466738613150456406110678471734535950128587177025434852253454027391670254414720755208170628139348782621305337642902757969178302363299705312962467498906684201941079348272346570045325840660432411041132963383252571828402313991299989578113948458447802731841283104264235648208841
Thanks so much,
Kostas
Such factorizations are necessary to find primitive polinomials of order k in the prime base M. This means that there are many problems in applied math that can benefit from this.
At this point many smallish k have been done, I am currently looking to finish k=120 but also some others if indeed help is on the way.
For k=120 there is only one factor remaining but it is a hard one c281, at the moment ECM with approx thousand curves at 260E6 have been run.
<c281> is
29921110466738613150456406110678471734535950128587177025434852253454027391670254414720755208170628139348782621305337642902757969178302363299705312962467498906684201941079348272346570045325840660432411041132963383252571828402313991299989578113948458447802731841283104264235648208841
Thanks so much,
Kostas
Re: help wanted: "Mersenne-Base Cunningham numbers"
Is there a discussion in mersenneforum.org about it? You should discuss it there first.
yoyo
yoyo
Re: help wanted: "Mersenne-Base Cunningham numbers"
yes i have asked there few weeks ago, some people have helped with the other numbers, as far as i can tell they like NFS jobs, this is too large for NFS. At the moment the attention to my request has diminished, maybe i should make bigger lists and let people decide what they want to run. But my situation is a little different, I dont factor just for fun, it is for a specific reason, to check primitivity of some polynomials in GF[M61] and I need order 120 next. Of course later i may want order 240 or 210 but those have remaining composite factors with 700-900 digits.
http://www.mersenneforum.org/showthread.php?t=17666
Anyway, if someone wants a bigger list to choose from, they are here, but take k which has itself prime factors less than < 13.
Such as k=35, 70, 80, 84, 96, 105, 168, ... anyway, those that have had work done on them already.
http://factordb.com/index.php?query=M61 ... &sent=Show
http://www.mersenneforum.org/showthread.php?t=17666
Anyway, if someone wants a bigger list to choose from, they are here, but take k which has itself prime factors less than < 13.
Such as k=35, 70, 80, 84, 96, 105, 168, ... anyway, those that have had work done on them already.
http://factordb.com/index.php?query=M61 ... &sent=Show
Re: help wanted: "Mersenne-Base Cunningham numbers"
How many curves at which B1 do you need for this c281?
Re: help wanted: "Mersenne-Base Cunningham numbers"
Hi yoyo, and thank you for any and all help. This number needs another 12000 curves at 1E8. If this does not crack it, then the next line in the optimal parameters table says 60 digit factors need 42000 curves at 260E6 .
Kostas
Kostas
Re: help wanted: "Mersenne-Base Cunningham numbers"
Ok, I queued 12000 curves @110M. It will show up in the aliquiot queue.
yoyo
yoyo
Re: help wanted: "Mersenne-Base Cunningham numbers"
Thanks, I can see it, good progress already. K
Re: help wanted: "Mersenne-Base Cunningham numbers"
Thanks for the help. Though a factor was not found, but excluding the factors of less than 55 digits is also of some importance in the problem i am trying to solve. Is it possible to schedule 42000 curves at 260E6 ?
Re: help wanted: "Mersenne-Base Cunningham numbers"
I'll will queue them.
yoyo
yoyo
Re: help wanted: "Mersenne-Base Cunningham numbers"
Fantastic news, Vielen Dank!!!
This will allow me to put out the new version of MIXMAX, my Random Number Generator, which is at http://mixmax.hepforge.org/, check it out.
This will allow me to put out the new version of MIXMAX, my Random Number Generator, which is at http://mixmax.hepforge.org/, check it out.