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2011-08-03, 16:13   #12
wblipp

"William"
May 2003
New Haven

2·32·131 Posts

Quote:
 Originally Posted by CRGreathouse If you reduce mod the Mersenne number at each step, you can prove 2^19 - 1 prime in Excel.
If you get the ZMath Addin, you can confirm 2^607-1 is prime in Excel. You can test up to 2^829-1.

2011-08-03, 18:21   #13
CRGreathouse

Aug 2006

2×3×977 Posts

Quote:
 Originally Posted by LiquidNitrogen What would this involve doing it the way you mentioned?
Every time you would square and subtract two, reduce mod p afterward. That way you're never squaring a number larger than p.

2011-08-03, 21:46   #14
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by CRGreathouse Every time you would square and subtract two, reduce mod p afterward. That way you're never squaring a number larger than p.
I thought it was mod 2^p-1 okay.

2011-08-04, 00:36   #15
LiquidNitrogen

Jun 2011
Henlopen Acres, Delaware

7×19 Posts

Quote:
 Originally Posted by CRGreathouse Every time you would square and subtract two, reduce mod p afterward. That way you're never squaring a number larger than p.
Ok, so I think I have it now. Is this spreadsheet correct then?

lucas lehmer.zip

2011-08-04, 00:43   #16
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by LiquidNitrogen Ok, so I think I have it now. Is this spreadsheet correct then? Attachment 6875

as far as I can tell yes. haven't checked the correct values on the way.

http://oeis.org/A095847

2011-08-04, 00:49   #17
LiquidNitrogen

Jun 2011
Henlopen Acres, Delaware

7×19 Posts

Quote:
 Originally Posted by wblipp If you get the ZMath Addin, you can confirm 2^607-1 is prime in Excel. You can test up to 2^829-1.
Now that is cool, thanks! Do you have that factor.exe program that is being referred to in the documentation? I went to the website it was linked to, but that site is down now.

Why can't authors just "bundle", all these external links are a drag!

2011-08-04, 01:08   #18
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

100000110000002 Posts

Quote:
 Originally Posted by LiquidNitrogen Now that is cool, thanks! Do you have that factor.exe program that is being referred to in the documentation? I went to the website it was linked to, but that site is down now. Why can't authors just "bundle", all these external links are a drag!

2011-08-04, 02:58   #19
LaurV
Romulan Interpreter

Jun 2011
Thailand

863510 Posts

Quote:
 Originally Posted by LiquidNitrogen And now I actually know how to do the Lucas-Lehmer test, although those s(k) numbers grow too big for Excel after s(4). At least Excel can prove 2^5 - 1 is prime using Lucas-Lehmer
in fact, using 32bit excel you can prove m=2^p-1 is prime for p=31 (and all p smaller, of course), using some tricks, like taking the MOD function each time, after each step (yes, there is a MOD function, you don't need to do division as said in another reply above) and using the fact that x^2=(m-x)^2 mod m (that is, testing after each step and taking the smallest one for squaring), and if you use VBA in excel and declare them as "variants", then you can go to 2^43-1 (that is proved composite). For 64bit excel you can go to prove m=2^p-1 is prime for p=61 (and all other primes p smaller then 61, leading to primes or composite m's) by declaring them as Longlong in VBA (this type is missing in Excel32).

This just for fun :D (no computational value).

Last fiddled with by LaurV on 2011-08-04 at 02:59

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