Assorted formulas for exponents of Mersenne primes

I have found a 39-digit exponent (which obviously cannot be revealed to any member of the public) but because of the 10-digit integer float of Prime95, it is not recognized as a prime number and hence i cannot submit. I have also found a Mersenne Prime generating function as well. Please reply to me so that i can submit my findings.

Thank you so much.

[Lee Yiyuan]

I have found a 39-digit exponent but i cannot submit it in Prime95 because of the 10 digit integer floating limitation which causes it to be recognized as a non-prime. I have also found a Mersenne Prime generating function, which i am sure you would be interested to know.

I hope you can reply to me via email or any other means ASAP. Thanks.

[Lee Yiyuan]

Does this program support exponents more than 10 digits? I have found an exponent that is 39 digits long. I have also found out a Mersenne prime generating formula.

[ET_]

Originally Posted by Lee Yiyuan

Does this program support exponents more than 10 digits? I have found an exponent that is 39 digits long. I have also found out a Mersenne prime generating formula.

It doesn't at the moment. But if you let me know your exponent via PM (private messaging) or email, I can set a trial-factor session with my program to double-check your assumption.

Luigi

[science_man_88]

Originally Posted by Lee Yiyuan

I have found a 39-digit exponent (which obviously cannot be revealed to any member of the public) but because of the 10-digit integer float of Prime95, it is not recognized as a prime number and hence i cannot submit. I have also found a Mersenne Prime generating function as well. Please reply to me so that i can submit my findings.

Thank you so much.

can you prove that the formula hold weight ?

[R.D. Silverman]

Originally Posted by Lee Yiyuan

I have found a 39-digit exponent but i cannot submit it in Prime95 because of the 10 digit integer floating limitation which causes it to be recognized as a non-prime. I have also found a Mersenne Prime generating function, which i am sure you would be interested to know.

I hope you can reply to me via email or any other means ASAP. Thanks.

Just what we don't need: Another Crank

[science_man_88]

Originally Posted by R.D. Silverman

Just what we don't need: Another Crank

like I've said before if you didn't want us here you'd be smart enough to make an test to stop us getting in.

[Uncwilly]

Originally Posted by Lee Yiyuan

I have also found a Mersenne Prime generating function as well. Please reply to me so that i can submit my findings.

Please post a copy of your method here (as a pdf, txt, or doc attachment.) That way it will placed a public place and no one can then claim that they did it first.
Also, if you have found a prime that is very large, can you please at least tell us the following:

• What hardware did you use to run your test?
• Did you write your own software?
• Did you check your number by trial division up to at least 85 bits?
• Did you run P-1 factoring or ECM on the number? (If so at what bounds?)
• How does your program perform the L-L test? (FFT's and such)
• If your test program does not perform a Lucas test, why not?

[science_man_88]

Originally Posted by Uncwilly

Please post a copy of your method here (as a pdf, txt, or doc attachement.) That way it will placed a public place and no one can then claim that they did it first.
Also, if you have found a prime that is very large, can you please at least tell us the following:

• What hardware did you use to run your test?
• Did you write your own software?
• Did you check your number by trial division up to at least 85 bits?
• Did you run P-1 factoring or ECM on the number? (If so at what bounds?)
• How does your program perform the L-L test? (FFT's and such)
• If your test program does not perform a Lucas test, why not?

I've heard it all before and thought what uncwilly said was a joke but I get why they say it because, by putting it out there first it's almost like claiming a copyright. I myself have interest in seeing your formula because i myself have played around quite a bit with mersenne prime exponents and haven't found much that could help.

[TimSorbet]

[nitpick ahead]

Originally Posted by Uncwilly

• Did you check your number by trial division up to at least 85 bits?

Assuming it is a Mersenne number with a prime exponent (something cranks have trouble doing ) that has 39 digits, the potential factors would start at 128 bits in size, so 100% of candidates meeting these requirements can be factored to not just 85, but 127 bits without any factors. How about 35 bits beyond the minimum, or ~164 bits. Note that this only has a ~25% chance of finding at least one factor, even if the claim of primality is false, so it's not a strong 'negative' result even if no factor is found. If you were to then extend this from 164 to 180 bits, which would be MUCH harder than 0 to 164, would only have a 9% chance of finding a factor.

Using currently known methods, a Mersenne number with a 39 digit exponent can not be known to be prime. Besides Prime95's limitation, it would take years. Hundreds of years on the best computer you could find, at minimum. You could have a ~25% chance of proving it composite fairly easily, by TFing, and of course any Mersenne number with a composite exponent is trivially composite, but proving primality is far harder.

[CRGreathouse]

Originally Posted by science_man_88

I've heard it all before and thought what uncwilly said was a joke but I get why they say it because, by putting it out there first it's almost like claiming a copyright.

In fact, if like science_man_88 and myself, the OP lives in a Berne signatory state then just by writing it a copyright is created. But if taken to court you'd need to prove copyright, so your choices would be to either make it public somewhere that records dates (say, on the mersenne forums) or, better but more expensive, register a copyright. In my country, this can be as cheap as $35.