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2010-05-21, 00:48
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#1 |
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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? |
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2010-05-21, 08:26
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#2 |
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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? |
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2010-05-21, 08:54
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#3 | |
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May 2010
2·3 Posts |
Quote:
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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2010-05-21, 10:12
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#4 | |
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May 2010
2×3 Posts |
Quote:
My bad Last fiddled with by Thiele on 2010-05-21 at 10:14 |
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2010-05-21, 10:18
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#5 |
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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" |
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2010-05-21, 11:08
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#6 |
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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. :)
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2010-05-21, 12:18
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#7 | |
"Bob Silverman"
Nov 2003
North of Boston
165248 Posts |
Quote:
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2010-05-21, 12:34
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#8 | |
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May 2010
2×3 Posts |
Quote:
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2010-05-21, 12:39
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#9 |
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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 |
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2010-05-21, 12:59
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#10 | |
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"Bob Silverman"
Nov 2003
North of Boston
22·1,877 Posts |
Quote:
it does not even present the conjecture. Instead one must fetch a file containing the conjecture. --> 2 levels of indirection. |
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2010-05-21, 13:06
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#11 |
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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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