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Old 2010-03-04, 21:42   #1
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Default Lucas-Lehmer test proof etc.

First if possible I'd like a link to PARI ( suggested last time I posted on here) I've reformatted since then I don't see how to install it! I was looking about the proof of the Lucas Lehmer test and I know it proves that the s values that show primality are all multiples of the prime they prove ( or I think it was that). This got me thinking to figure out what multiplies by the primes to get these results and I came across 607 another prime Mersenne exponent. I was going to suggest it might be a way to find higher Mersenne exponents ( not a good idea on here) but can anyone help verify at least that all the other results of the divisions are prime ? maybe then I'll see if I can find a proof of Mersenne Prime exponents in them all.

Last fiddled with by science_man_88 on 2010-03-04 at 21:43
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Old 2010-03-04, 21:48   #2
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All of the results of ?
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Old 2010-03-04, 21:52   #3
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the results like 14/(7*2) and s(3)/(31*2) where s is it's value in the lehmer test. I'm multiplying by 2 on bottom as I find that the results I see so far divide by 2 at least

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Old 2010-03-04, 23:08   #4
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Default Ok..

Not sure where you are going.. but

MP2 -- 4/ (3 * 2) = 0


MP3 -- 14/ (7 * 2) = 1
S(2) = 14


MP5 -- 62/ (31 * 2) = 1
S(2) = 14
S(3) = 194
S(4) = 62


MP7 -- 12319/ (127 * 2) = 48
S(2) = 14
S(3) = 194
S(4) = 4487
S(5) = 1762
S(6) = 12319


MP11 -- 79522/ (2047 * 2) = 19
S(2) = 14
S(3) = 194
S(4) = 37634
S(5) = 620942
S(6) = 491399
S(7) = 14159
S(8) = 3523127
S(9) = 57598
S(10) = 79522
You do realize that that last s should be MOD MP and = 0 when MP is prime... but the rest of prime P < 64 see...

http://dotnetmath.alexanderhiggins.c...jecture_a.aspx
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Old 2010-03-04, 23:38   #5
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not exactly where I wanted to go I was going more for:

http://www.research.att.com/~njas/sequences/A003010

when divided by the proper

id:A000668 seems when divided by 2 to give a prime(asking for verification of that) (in fact one I tried gave 607(a mersenne prime exponent))

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Old 2010-03-04, 23:47   #6
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Quote:
Originally Posted by alexhiggins732 View Post
Not sure where you are going.. but

MP2 -- 4/ (3 * 2) = 0


MP3 -- 14/ (7 * 2) = 1
S(2) = 14


MP5 -- 62/ (31 * 2) = 1
S(2) = 14
S(3) = 194
S(4) = 62


MP7 -- 12319/ (127 * 2) = 48
S(2) = 14
S(3) = 194
S(4) = 4487
S(5) = 1762
S(6) = 12319


MP11 -- 79522/ (2047 * 2) = 19
S(2) = 14
S(3) = 194
S(4) = 37634
S(5) = 620942
S(6) = 491399
S(7) = 14159
S(8) = 3523127
S(9) = 57598
S(10) = 79522
You do realize that that last s should be MOD MP and = 0 when MP is prime... but the rest of prime P < 64 see...

http://dotnetmath.alexanderhiggins.c...jecture_a.aspx
funny how when I've seen it it was s(0)=4 and done until s(p-2) to give a residue of 1736 for 2047.

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Old 2010-03-04, 23:49   #7
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I know mini geek is just waiting to get someone to delete this lol
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Old 2010-03-04, 23:50   #8
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Quote:
Originally Posted by science_man_88 View Post
funny how when I've seen it it was s(0)=4 and done until s(p-2) to give a residue of 1736 for 2047.
If you start at index 0 and go to index p-2, it's the same as starting at index 1 and going to index p-1. Some sources say to start at 0, some at 1. Neither is right or wrong, really.
Quote:
Originally Posted by science_man_88 View Post
I know mini geek is just waiting to get someone to delete this lol
Now why would I want that? As long as it's kept to the Misc Math forum, I'm fine with it. Sometimes I even find these threads amusing (in a way).

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Old 2010-03-04, 23:52   #9
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Do You get what I'm talking about Mini-Geek ?
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Old 2010-03-04, 23:57   #10
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mini geek also if you look he went from 2 to p-1 most times
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Old 2010-03-05, 00:07   #11
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14/7 = 2 2/2=1
37634/31=1214 1214/2 = 607 <- prime exponent
2005956546822746114/127 = 15794933439549182 that / 2 = 7897466719774591<- possible prime exponent ?

basically I'm trying to find a way to use

http://www.research.att.com/~njas/sequences/A003010 to find something useful ( such as exponents that work)
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