How to check if a number is a Mersenne prime ?

2004-06-18, 07:34

What do I do if I think I have found a greater mersenne but my calculator has no way to check it, or I don't. (It can only do 2^400 or something...)

Is there a fairly easy way to check whether I have one or not with a program? I tried downloading 'ntprime' but I don't know how it works, it didn't seem to do anything...

MrHappy · 2004-06-18, 09:20

A Mersenne number (-> just check if the exponent is prime) or a Mersenne prime? For the latter: download Prime95 Version 23.8 from http://www.mersenne.org/freesoft.htm and enter the exponent in [Prime95]->[Advanced]->[Test]. If you don't see immedite progress just lower the entry in [Prime95]->[Options]->[Preferences]->[Iterations between screen outputs].

Prime95 works for exponents up to 79 300 000.

MrHappy.

Uncwilly · 2004-06-18, 13:37

You can find a list of all known Mersenne primes here: http://www.utm.edu/research/primes/m...dex.html#known

Also, know that:

Quote:

All exponents below 8,715,700 have been tested and double-checked.

This means that there are no unknown Meresenne primes lurking below that value.

2004-06-18, 16:14

that's what u think!!

PrimeCruncher · 2004-06-18, 20:40

I think our tests are fairly conclusive. We keep testing the exponent until we get two matching residues. Version 23 implements error codes so we can tell if a test is probably bad.

Uncwilly · 2004-06-18, 20:55

Yes, I think that the matching residues is key here. To have these 2 large numbers to happen to match and one be an erroneous test is highly unlikely. To have 2 that have errors that match is so unlikely that it is considered to be all but magical. The actual chances are around.

Having a second type of hardware with a second program check this with the same residue is considered proof for the math community.

2004-06-19, 08:18

Ok I had the wrong program before, that one worked, thanks.
I was attemptimng one much higher than 8 mil, more like 54 million or something but it wasn't even a prime number so no luck... Thanks anyway.

2004-06-18, 07:34	#1
Unregistered 5·673 Posts	How to check if a number is a Mersenne prime ? What do I do if I think I have found a greater mersenne but my calculator has no way to check it, or I don't. (It can only do 2^400 or something...) Is there a fairly easy way to check whether I have one or not with a program? I tried downloading 'ntprime' but I don't know how it works, it didn't seem to do anything...

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2004-06-18, 09:20	#2
MrHappy Dec 2003 Paisley Park & Neverland 185₁₀ Posts	A Mersenne number (-> just check if the exponent is prime) or a Mersenne prime? For the latter: download Prime95 Version 23.8 from http://www.mersenne.org/freesoft.htm and enter the exponent in [Prime95]->[Advanced]->[Test]. If you don't see immedite progress just lower the entry in [Prime95]->[Options]->[Preferences]->[Iterations between screen outputs]. Prime95 works for exponents up to 79 300 000. MrHappy.

2004-06-18, 16:14	#4
Unregistered 1101010000001₂ Posts	that's what u think!!

2004-06-18, 20:40	#5
PrimeCruncher Sep 2003 Borg HQ, Delta Quadrant 702₁₀ Posts	I think our tests are fairly conclusive. We keep testing the exponent until we get two matching residues. Version 23 implements error codes so we can tell if a test is probably bad.

2004-06-18, 20:55	#6
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2×47×113 Posts	Yes, I think that the matching residues is key here. To have these 2 large numbers to happen to match and one be an erroneous test is highly unlikely. To have 2 that have errors that match is so unlikely that it is considered to be all but magical. The actual chances are around. Having a second type of hardware with a second program check this with the same residue is considered proof for the math community.

2004-06-19, 08:18	#7
Unregistered 2³×3×307 Posts	Ok I had the wrong program before, that one worked, thanks. I was attemptimng one much higher than 8 mil, more like 54 million or something but it wasn't even a prime number so no luck... Thanks anyway.