Lucas-Lehmer test proof etc.

science_man_88 · 2010-03-04, 21:42

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.

alexhiggins732 · 2010-03-04, 21:48

All of the results of ?

science_man_88 · 2010-03-04, 21:52

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

alexhiggins732 · 2010-03-04, 23:08

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

science_man_88 · 2010-03-04, 23:38

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))

science_man_88 · 2010-03-04, 23:47

Quote:

Originally Posted by alexhiggins732

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.

science_man_88 · 2010-03-04, 23:49

I know mini geek is just waiting to get someone to delete this lol

TimSorbet · 2010-03-04, 23:50

Quote:

Originally Posted by science_man_88

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

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).

science_man_88 · 2010-03-04, 23:52

Do You get what I'm talking about Mini-Geek ?

science_man_88 · 2010-03-04, 23:57

mini geek also if you look he went from 2 to p-1 most times

science_man_88 · 2010-03-05, 00:07

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)

2010-03-04, 21:42	#1
science_man_88 "Forget I exist" Jul 2009 Dartmouth NS 20342₈ Posts	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

2010-03-04, 21:52	#3
science_man_88 "Forget I exist" Jul 2009 Dartmouth NS 2·3·23·61 Posts	the results like 14/(72) and s(3)/(312) 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 Last fiddled with by science_man_88 on 2010-03-04 at 21:53

2010-03-04, 23:08	#4
alexhiggins732 Mar 2010 Brick, NJ 67 Posts	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

2010-03-04, 23:38	#5
science_man_88 "Forget I exist" Jul 2009 Dartmouth NS 20E2₁₆ Posts	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)) Last fiddled with by science_man_88 on 2010-03-04 at 23:39

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2010-03-04, 21:48	#2
alexhiggins732 Mar 2010 Brick, NJ 67 Posts	All of the results of ?

2010-03-04, 23:49	#7
science_man_88 "Forget I exist" Jul 2009 Dartmouth NS 2×3×23×61 Posts	I know mini geek is just waiting to get someone to delete this lol

2010-03-04, 23:52	#9
science_man_88 "Forget I exist" Jul 2009 Dartmouth NS 8418₁₀ Posts	Do You get what I'm talking about Mini-Geek ?

2010-03-04, 23:57	#10
science_man_88 "Forget I exist" Jul 2009 Dartmouth NS 8418₁₀ Posts	mini geek also if you look he went from 2 to p-1 most times

2010-03-05, 00:07	#11
science_man_88 "Forget I exist" Jul 2009 Dartmouth NS 2·3·23·61 Posts	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)