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Old 2010-05-21, 00:48   #1
Thiele
 
May 2010

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Default 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?
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Old 2010-05-21, 08:26   #2
ATH
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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?
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Old 2010-05-21, 08:54   #3
Thiele
 
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Quote:
Originally Posted by ATH View Post
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.
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Old 2010-05-21, 10:12   #4
Thiele
 
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Quote:
Originally Posted by Thiele View Post
n = 2^(log_2(m))
Was a little typo. It should be: 2^(ceil(log_2(m)))

My bad

Last fiddled with by Thiele on 2010-05-21 at 10:14
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Old 2010-05-21, 10:18   #5
ATH
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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"
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Old 2010-05-21, 11:08   #6
Thiele
 
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Fair point. I corrected it so that it now says 3^x, which was intended, and uploaded a new copy. :)
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Old 2010-05-21, 12:18   #7
R.D. Silverman
 
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Quote:
Originally Posted by Thiele View Post
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?
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Old 2010-05-21, 12:34   #8
Thiele
 
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Quote:
Originally Posted by R.D. Silverman View Post
Why are you being furtive about it?
Furtive? About what?
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Old 2010-05-21, 12:39   #9
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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
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Old 2010-05-21, 12:59   #10
R.D. Silverman
 
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Quote:
Originally Posted by Thiele View Post
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.
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Old 2010-05-21, 13:06   #11
retina
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Thiele wants to track visitors to the site?
Or maybe earn some advertising money by attracting viewers to the site?
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