Math Is Fun Forum

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

Mersenne Primes.

Hello

I am doing some work on some Mersenne primes and can't figure out the following;

Why is this always divisible by p when p is prime?

---

"Time not important. Only life important." - The Fifth Element 1997

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mersenne Primes.

Hi;

That is called Fermat's little theorem and was stated by him around 1640. The theorem states

If p is a prime and a is any integer not divisible by p, then

is divisible by p.

In your case you are choosing a = 2 and all the primes greater than 2 satisfy the condition of not dividing 2.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

Re: Mersenne Primes.

Thanks so much!

Now I can continue with my mersenne prime theorem.

---

"Time not important. Only life important." - The Fifth Element 1997

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mersenne Primes.

Hi;

You might want to take a look at some of what is already known about them here:

http://primes.utm.edu/mersenne/index.html

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.