20100521, 00:48  #1 
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 counterexamples? 
20100521, 08:26  #2 
Einyen
Dec 2003
Denmark
2×3×13×41 Posts 
I can't see how you get those numbers.
For example p=17: Mp = 2^171 = 131071 x = 131070/17 = 7710 m = 8192  7710 = 482 m = 482 (mod Mp), not 0 as you write? 
20100521, 08:54  #3 
May 2010
2×3 Posts 

20100521, 10:12  #4 
May 2010
6_{16} Posts 
Was a little typo. It should be: 2^(ceil(log_2(m)))
My bad Last fiddled with by Thiele on 20100521 at 10:14 
20100521, 10:18  #5 
Einyen
Dec 2003
Denmark
C7E_{16} 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" 
20100521, 11:08  #6 
May 2010
6_{16} Posts 
Fair point. I corrected it so that it now says 3^x, which was intended, and uploaded a new copy. :)

20100521, 12:18  #7  
Nov 2003
2^{2}×5×373 Posts 
Quote:


20100521, 12:34  #8 
May 2010
2×3 Posts 

20100521, 12:39  #9 
Einyen
Dec 2003
Denmark
C7E_{16} 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 20100521 at 12:40 
20100521, 12:59  #10 
Nov 2003
1110100100100_{2} Posts 

20100521, 13:06  #11 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2·23·137 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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