Continuity of Primes

[wblipp]

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.

[CRGreathouse]

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.

[science_man_88]

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.

[LiquidNitrogen]

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

[science_man_88]

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

[LiquidNitrogen]

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!

[science_man_88]

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!

inurl:"factor.exe" might help in google.

[LaurV]

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).