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
3,413 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
3,413 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
110_{2} 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  
"Bob Silverman"
Nov 2003
North of Boston
2^{3}·937 Posts 
Quote:


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

20100521, 12:39  #9 
Einyen
Dec 2003
Denmark
3413_{10} 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 
"Bob Silverman"
Nov 2003
North of Boston
2^{3}×937 Posts 

20100521, 13:06  #11 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{4}×5×83 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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