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 2018-02-02, 16:22 #1 sudaprime   Feb 2018 116 Posts probable largest prime. complexions in computing ristricts calculating the probable largest prime, in Mersenne's series. the series goes like this. M3 = 7 is prime. (M2 = 3, starting from 2, is prime and M3= M(M2)) M7 = 127 is prime, ( or M7= M(M3) ) M127 = 1.7e38 is prime or( M127= M(M7)) and it is most likely that, M(M127) is a prime. practically it takes ages to devolop a machine to calculate M(M127) then it takes more to test whether its a prime or not. we can not test this at this time.
 2018-02-02, 17:45 #2 paulunderwood     Sep 2002 Database er0rr 2×5×467 Posts Therefore $M^n(2)$ is prime for all n>0. This could be similar to the mistake Fermat made for $2^{2^n}+1$ Last fiddled with by paulunderwood on 2018-02-02 at 17:49
 2018-02-02, 17:53 #3 science_man_88     "Forget I exist" Jul 2009 Dartmouth NS 2·52·132 Posts The double mersenne numbers follow 2*x^2+4*x+1 if I knew how to apply this a certain number of times easily, we could find polynomials that these Catalan mersennes are on.
2018-02-02, 17:57   #4
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

3×37×61 Posts

Quote:
 Originally Posted by sudaprime ... it is most likely that, M(M127) is a prime.
I expect the likelihood of it being prime is the opposite of what you claim. Being such a large number I find it more likely to be composite. I base this on my unmathematical observation that there are a great many possible numbers that could be a divisor. I see no reason to put any credence into an apparent progression length of only four.

 2018-02-02, 18:47 #5 CRGreathouse     Aug 2006 22×3×499 Posts I don't know if more recent work has been done, but Double Mersennes Prime Search has searched k < 111e15: http://www.doublemersennes.org/mm127.php This means that MM127 has no prime factors below 2*k*M127 = 3.777... * 10^55, which in turn means that it's exp(gamma)*log(3.777... * 10^55) ~ 228 times more likely to be likely than an average number of its size.* This raises the 'probability' of it being prime from 1/log(MM127) to 228/log(MM127) ~ 228/(M127 * log 2) which is a little less than 2 in 10^36. For comparison, you're 438 times more likely to win all of the Powerball, Mega Millions, Eurojackpot, and EuroMillions jackpots buying just one ticket each. * This can be made precise in the usual way.
 2018-02-02, 22:15 #6 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 101011000011112 Posts
2018-02-02, 22:22   #7
danaj

"Dana Jacobsen"
Feb 2011
Bangkok, TH

2×5×7×13 Posts

Quote:
 Originally Posted by CRGreathouse For comparison, you're 438 times more likely to win all of the Powerball, Mega Millions, Eurojackpot, and EuroMillions jackpots buying just one ticket each.
So you're saying there's a chance. Keep the dream alive!

 2018-02-03, 02:52 #8 VBCurtis     "Curtis" Feb 2005 Riverside, CA 2·5·7·83 Posts Since 3 makes a pattern according to the OP, here is a way to find an even larger prime: 3, 5, and 7 are all prime. By continuing this pattern of adding two every time, all odd numbers are prime. Woot!
2018-02-03, 05:00   #9
ATH
Einyen

Dec 2003
Denmark

2×3×52×23 Posts

Quote:
 Originally Posted by CRGreathouse For comparison, you're 438 times more likely to win all of the Powerball, Mega Millions, Eurojackpot, and EuroMillions jackpots buying just one ticket each. * This can be made precise in the usual way.
If I'm that likely to win all those, I might even win without buying tickets!!!

I did actually win the Eurojackpot tonight, seriously!!!

though I did not win the huge 570M dkk jackpot. I won 83 dkk (~\$14).

2018-02-03, 05:59   #10
CRGreathouse

Aug 2006

135448 Posts

Quote:
 Originally Posted by VBCurtis 3, 5, and 7 are all prime. By continuing this pattern of adding two every time, all odd numbers are prime. Woot!
https://xkcd.com/1310/

 2018-02-03, 06:02 #11 retina Undefined     "The unspeakable one" Jun 2006 My evil lair 3·37·61 Posts Okay, so to summarise this thread it appears that the way to prove MM127 is prime is to simply win all of the Powerball, Mega Millions, Eurojackpot, and EuroMillions jackpots 438 times. That seems doable. The only downside is becoming a multi-multi-billionaire. Oh well, nothing is perfect.

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