mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Miscellaneous Math

Reply
 
Thread Tools
Old 2005-11-11, 00:05   #1
pacionet
 
pacionet's Avatar
 
Oct 2005
Italy

15316 Posts
Default General formula

Is it possible that a general formula exist for all Mersenne primes ?
pacionet is offline   Reply With Quote
Old 2005-11-11, 00:55   #2
ewmayer
2ω=0
 
ewmayer's Avatar
 
Sep 2002
Rep├║blica de California

22×3×7×139 Posts
Default

If you're talking about all that are known *and* those yet to be found, then it's exceedingly improbable. Finding a formula that yields all that are already known (say a smooth function f(x) such that f(n) gives the exponent of the (n)th Mersenne prime) is of course a (rather silly) exercise in curve fitting.
ewmayer is offline   Reply With Quote
Old 2005-11-11, 09:43   #3
Orgasmic Troll
Cranksta Rap Ayatollah
 
Orgasmic Troll's Avatar
 
Jul 2003

28116 Posts
Default

of course there is. M(n) where M(n) is the n-th Mersenne prime. if you don't mind filtering through results, you can even write M'(n) where M'(n) = 2^n-1. I guarantee you that every mersenne prime will be listed, you just have to disregard the composite mersenne numbers
Orgasmic Troll is offline   Reply With Quote
Old 2005-11-11, 13:57   #4
pacionet
 
pacionet's Avatar
 
Oct 2005
Italy

15316 Posts
Default

Quote:
Originally Posted by TravisT
of course there is. M(n) where M(n) is the n-th Mersenne prime. if you don't mind filtering through results, you can even write M'(n) where M'(n) = 2^n-1. I guarantee you that every mersenne prime will be listed, you just have to disregard the composite mersenne numbers

I mean , of course, a formula f(n) where , when n varies , f(n) returns a Mersenne prime number (for all n values)
pacionet is offline   Reply With Quote
Old 2005-11-11, 14:23   #5
R.D. Silverman
 
R.D. Silverman's Avatar
 
Nov 2003

746010 Posts
Default

Quote:
Originally Posted by pacionet

I mean , of course, a formula f(n) where , when n varies , f(n) returns a Mersenne prime number (for all n values)
Yes. Such a formula exists. But it is *useless* for computational
purposes.

I will give a hint how to construct such a formula.

Let the n'th Mersenne prime be given as M(n) = 2^(p_n) - 1
where p_n is the exponent of the n'th prime.

Consider the constant:

alpha = sum(i=1 to oo) of 10^(-2i) p_i. This is a well defined
real number. The sum clearly converges.

Now, given this constant, one can compute M(n) by multiplying
alpha by 10^(2n), extracting the fractional part
of 10^(2n) alpha, subtracting then truncating the part of the fraction after the trailing 0's that follow p_n. One can do this with a suitable
combination of floor functions and simple multiplications that I am too
lazy to work out at the moment. A similar formula may be found in
Hardy and Wright except it gives the n'th prime, instead of the n'th
Mersenne prime.


It is useless, because we have no way of computing alpha to find
as yet unknown primes.

But the formula does indeed *exist* because alpha exists.
R.D. Silverman is offline   Reply With Quote
Old 2005-12-04, 17:31   #6
sghodeif
 
Sep 2005

228 Posts
Default we find this

of course there is.2^F-1 where F one of Fermates prime numbers(in special form) .
sghodeif is offline   Reply With Quote
Old 2005-12-04, 18:11   #7
akruppa
 
akruppa's Avatar
 
"Nancy"
Aug 2002
Alexandria

9A316 Posts
Default

sghodeif, what exactly are you referring to, what precisely do you mean by "special form" and how do Fermat numbers enter the picture?

Alex
akruppa is offline   Reply With Quote
Old 2005-12-04, 22:05   #8
ewmayer
2ω=0
 
ewmayer's Avatar
 
Sep 2002
Rep├║blica de California

22×3×7×139 Posts
Default

Quote:
Originally Posted by akruppa
sghodeif, what exactly are you referring to, what precisely do you mean by "special form" and how do Fermat numbers enter the picture?
sghodeif is simply trying very hard to get this thread moved to the "miscellaneous math threads forum," Alex.
ewmayer is offline   Reply With Quote
Old 2005-12-04, 22:52   #9
Citrix
 
Citrix's Avatar
 
Jun 2003

5·317 Posts
Default

I think he is telling us that he needs coffee, as the icon says.

Citrix
Citrix is offline   Reply With Quote
Old 2005-12-05, 08:02   #10
akruppa
 
akruppa's Avatar
 
"Nancy"
Aug 2002
Alexandria

2,467 Posts
Default

Well, lets not dismiss it without at least giving him a chance to explain himself.

Alex
akruppa is offline   Reply With Quote
Old 2005-12-05, 08:13   #11
Citrix
 
Citrix's Avatar
 
Jun 2003

5·317 Posts
Default

He might be saying that

2^(2^2^x)+1)-1 is always prime, for prime fermat's.

So 2^3-1 is prime
2^5-1 is prime
2^17-1 is prime
but 2^257-1 is not prime?

So still not sure.
Citrix is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
General Questions pastcow Factoring 10 2013-02-27 07:01
General Status??? R.D. Silverman NFSNET Discussion 4 2007-07-19 18:43
New LLT formula hoca Math 7 2007-03-05 17:41
general Mersenne Val 15k Search 10 2004-03-13 20:56
General Mersenne? TTn Miscellaneous Math 1 2003-08-26 03:14

All times are UTC. The time now is 12:17.


Fri Dec 3 12:17:20 UTC 2021 up 133 days, 6:46, 0 users, load averages: 0.67, 0.82, 0.90

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.