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
3435_{10} 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
2×3 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
3×5×229 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" 
20100521, 11:08  #6 
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. :)

20100521, 12:18  #7  
"Bob Silverman"
Nov 2003
North of Boston
16524_{8} Posts 
Quote:


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

20100521, 12:39  #9 
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 20100521 at 12:40 
20100521, 12:59  #10 
"Bob Silverman"
Nov 2003
North of Boston
2^{2}·1,877 Posts 

20100521, 13:06  #11 
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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