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 2010-05-21, 00:48 #1 Thiele   May 2010 2·3 Posts A conjecture on a new property of Mersenne primes I recently discovered a new property of Mersenne primes, which I wrote a little about and calculated some data about. The conjecture can be found at: http://thiele.nu/artikel.php?artikel=12 The data is far from comprehensive due to Java being slow a multiplying large numbers. So if anyone has a Java implementation of FFT or some other fast multiplying algorithm, I would very much appreciate it! Any feedback or counter-examples?
 2010-05-21, 08:26 #2 ATH Einyen     Dec 2003 Denmark 343510 Posts I can't see how you get those numbers. For example p=17: Mp = 2^17-1 = 131071 x = 131070/17 = 7710 m = 8192 - 7710 = 482 m = 482 (mod Mp), not 0 as you write?
2010-05-21, 08:54   #3
Thiele

May 2010

2·3 Posts

Quote:
 Originally Posted by ATH I can't see how you get those numbers. For example p=17: Mp = 2^17-1 = 131071 x = 131070/17 = 7710 m = 8192 - 7710 = 482 m = 482 (mod Mp), not 0 as you write?
Indeed. But:
m = 3^7710
n = 2^(log_2(m))
(n%m)%Mp = 0

For 17. Which is the way I get these numbers.

2010-05-21, 10:12   #4
Thiele

May 2010

2×3 Posts

Quote:
 Originally Posted by Thiele n = 2^(log_2(m))
Was a little typo. It should be: 2^(ceil(log_2(m)))

Last fiddled with by Thiele on 2010-05-21 at 10:14

 2010-05-21, 10:18 #5 ATH Einyen     Dec 2003 Denmark 3×5×229 Posts You need to rewrite your conjecture then, it says: m = n2(x) - x so where do you get 3^7710 from? Conjecture also says "m%Mp = 0" not "(n%m)%Mp=0"
 2010-05-21, 11:08 #6 Thiele   May 2010 2·3 Posts Fair point. I corrected it so that it now says 3^x, which was intended, and uploaded a new copy. :)
2010-05-21, 12:18   #7
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

165248 Posts

Quote:
 Originally Posted by Thiele I recently discovered a new property of Mersenne primes, which I wrote a little about and calculated some data about. The conjecture can be found at: http://thiele.nu/artikel.php?artikel=12 The data is far from comprehensive due to Java being slow a multiplying large numbers. So if anyone has a Java implementation of FFT or some other fast multiplying algorithm, I would very much appreciate it! Any feedback or counter-examples?
Why are you being furtive about it?

2010-05-21, 12:34   #8
Thiele

May 2010

2×3 Posts

Quote:
 Originally Posted by R.D. Silverman Why are you being furtive about it?

 2010-05-21, 12:39 #9 ATH Einyen     Dec 2003 Denmark 3×5×229 Posts p is only a factor of (Mp - 1) when Mp is prime, so x = (Mp - 1)/p is only an integer when Mp is prime. Last fiddled with by ATH on 2010-05-21 at 12:40
2010-05-21, 12:59   #10
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

22·1,877 Posts

Quote:
 Originally Posted by Thiele Furtive? About what?
Your conjecture. Rather than post it here, you referenced a URL, and
it does not even present the conjecture. Instead one must
fetch a file containing the conjecture. --> 2 levels of indirection.

 2010-05-21, 13:06 #11 retina Undefined     "The unspeakable one" Jun 2006 My evil lair 5·7·191 Posts Thiele wants to track visitors to the site? Or maybe earn some advertising money by attracting viewers to the site?

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