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Old 2004-06-18, 07:34   #1
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Default 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...
 
Old 2004-06-18, 09:20   #2
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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.

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Old 2004-06-18, 13:37   #3
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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.
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Old 2004-06-18, 16:14   #4
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that's what u think!!
 
Old 2004-06-18, 20:40   #5
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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.
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Old 2004-06-18, 20:55   #6
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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.
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Old 2004-06-19, 08:18   #7
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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.
 
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