A quick discussion of Mersenne Numbers

I wake of the latest find announcement, some people maybe wondering what the
heck is this?!!

A mercenne number is of the type:

M(p) = 2**p -1 results in a prime when p is a prime.

Hopefully this will lead the way to see the pattern of prime numbers and
being able to compute prime numbers in a far more efficient manner (after all
a function that when given a prime number results in a prime number would be
quite a kicker now wouldn't it!)

The other Mersenne primes include:

2,3,5,7,13,17,19,31,127,61,89, and 107.

The numbers 67 and 257 are not primes....

Have fun in them prime number databases....

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On Sun, 1 Dec 1996 Scottauge@aol.com wrote:

> I wake of the latest find announcement, some people maybe wondering what the
> heck is this?!!
> 
> A mercenne number is of the type:
> 
> M(p) = 2**p -1 results in a prime when p is a prime.
> 
> Hopefully this will lead the way to see the pattern of prime numbers and
> being able to compute prime numbers in a far more efficient manner (after all
> a function that when given a prime number results in a prime number would be
> quite a kicker now wouldn't it!)

It doesn't.  If q is a Mercenne prime, then p is prime if q = 2^p-1.  It
doesn't work the other way around.  If it did, then it would be very easy to
find out if a number is a Mercenne prime: just add 1 and find the base 2
logarithm and if the result is prime, then the original number is prime.  It's
much more difficult than that.  It would also be possible to find an infinite
number of Mercenne primes using a deterministic algorithm.


Mark
- -- 
finger -l for PGP key
PGP encrypted mail prefered.
0xf9b22ba5 now revoked

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On Sun, 1 Dec 1996 14:10:13 -0500, Scottauge@aol.com wrote:

   A mercenne number is of the type:

   M(p) = 2**p -1 results in a prime when p is a prime.

*Occasionally* results in a prime when p is prime.  (A Mersenne number
is any number of that form, prime or composite.  It so happens that if
M(p) is prime, p is prime)

   Hopefully this will lead the way to see the pattern of prime
   numbers and being able to compute prime numbers in a far more
   efficient manner (after all a function that when given a prime
   number results in a prime number would be quite a kicker now
   wouldn't it!)

That's easy: f(x) = x

   The other Mersenne primes include:

   2,3,5,7,13,17,19,31,127,61,89, and 107.

2, 5, 13, 17, 19, 61, 89 and 107 are not Mersenne numbers :-|

The first few Mersenne primes are:
3, 7, 31, 127, 8191, 131071, 524287, 2147483647

-- 
Paul Foley <mycroft@actrix.gen.nz>       ---         PGPmail preferred

	   PGP key ID 0x1CA3386D available from keyservers
    fingerprint = 4A 76 83 D8 99 BC ED 33  C5 02 81 C9 BF 7A 91 E8
----------------------------------------------------------------------
If God had wanted you to go around nude, He would have given you bigger
hands.

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On Mon, 2 Dec 1996, Paul Foley wrote:

> On Sun, 1 Dec 1996 14:10:13 -0500, Scottauge@aol.com wrote:
> 
>    A mercenne number is of the type:
> 
>    M(p) = 2**p -1 results in a prime when p is a prime.
> 
> *Occasionally* results in a prime when p is prime.  (A Mersenne number
> is any number of that form, prime or composite.  It so happens that if
> M(p) is prime, p is prime)
> 
>    Hopefully this will lead the way to see the pattern of prime
>    numbers and being able to compute prime numbers in a far more
>    efficient manner (after all a function that when given a prime
>    number results in a prime number would be quite a kicker now
>    wouldn't it!)
> 
> That's easy: f(x) = x
> 
>    The other Mersenne primes include:
> 
>    2,3,5,7,13,17,19,31,127,61,89, and 107.
> 
> 2, 5, 13, 17, 19, 61, 89 and 107 are not Mersenne numbers :-|
> 
> The first few Mersenne primes are:
> 3, 7, 31, 127, 8191, 131071, 524287, 2147483647

True.. but 1 is. 2^1-1=1


 --Deviant
   PGP KeyID = E820F015 Fingerprint = 3D6AAB628E3DFAA9 F7D35736ABC56D39

Try `stty 0' -- it works much better.


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On Mon, 2 Dec 1996, The Deviant wrote:

> On Mon, 2 Dec 1996, Paul Foley wrote:
> 
> > On Sun, 1 Dec 1996 14:10:13 -0500, Scottauge@aol.com wrote:
> >
> >    A mercenne number is of the type:
> >
> >    M(p) = 2**p -1 results in a prime when p is a prime.
> >
> > *Occasionally* results in a prime when p is prime.  (A Mersenne number
> > is any number of that form, prime or composite.  It so happens that if
> > M(p) is prime, p is prime)
> >
> >    Hopefully this will lead the way to see the pattern of prime
> >    numbers and being able to compute prime numbers in a far more
> >    efficient manner (after all a function that when given a prime
> >    number results in a prime number would be quite a kicker now
> >    wouldn't it!)
> >
> > That's easy: f(x) = x
> >
> >    The other Mersenne primes include:
> >
> >    2,3,5,7,13,17,19,31,127,61,89, and 107.
> >
> > 2, 5, 13, 17, 19, 61, 89 and 107 are not Mersenne numbers :-|
> >
> > The first few Mersenne primes are:
> > 3, 7, 31, 127, 8191, 131071, 524287, 2147483647
> 
> True.. but 1 is. 2^1-1=1

1 isn't prime.  It also isn't composite.  Same for zero.

Mark
-- 
finger -l for PGP key
PGP encrypted mail prefered.
0xf9b22ba5 now revoked

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On Mon, 2 Dec 1996, The Deviant wrote:

> On Mon, 2 Dec 1996, Paul Foley wrote:
> 
> > On Sun, 1 Dec 1996 14:10:13 -0500, Scottauge@aol.com wrote:
> >
> >    A mercenne number is of the type:
> >
> >    M(p) = 2**p -1 results in a prime when p is a prime.
> >
> > *Occasionally* results in a prime when p is prime.  (A Mersenne number
> > is any number of that form, prime or composite.  It so happens that if
> > M(p) is prime, p is prime)
> >
> >    Hopefully this will lead the way to see the pattern of prime
> >    numbers and being able to compute prime numbers in a far more
> >    efficient manner (after all a function that when given a prime
> >    number results in a prime number would be quite a kicker now
> >    wouldn't it!)
> >
> > That's easy: f(x) = x
> >
> >    The other Mersenne primes include:
> >
> >    2,3,5,7,13,17,19,31,127,61,89, and 107.
> >
> > 2, 5, 13, 17, 19, 61, 89 and 107 are not Mersenne numbers :-|
> >
> > The first few Mersenne primes are:
> > 3, 7, 31, 127, 8191, 131071, 524287, 2147483647
> 
> True.. but 1 is. 2^1-1=1
> 
> 
>  --Deviant
>    PGP KeyID = E820F015 Fingerprint = 3D6AAB628E3DFAA9 F7D35736ABC56D39
> 
> Try `stty 0' -- it works much better.

Please excuse me for writing such idiocy.  I was very tired at the time.

 --Deviant
   PGP KeyID = E820F015 Fingerprint = 3D6AAB628E3DFAA9 F7D35736ABC56D39

Insufficient facts always invite danger.
                -- Spock, "Space Seed", stardate 3141.9


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