# Thread: Primes from a pattern

1. ## Primes from a pattern

I am a math hobbyist working through John Stillwell's book "Elements of Number Theory"

On page 3 Stillwell after pointing out that $\displaystyle n^2 +n + 41$ is prime for all small values of n, poses the following problem:

"Show, nevertheless that $\displaystyle n^2 +n + 41$ is not prime for certain values of n"

Can anyone help me with this problem? I would certainly like to see a rigorous proof.

2. Originally Posted by Bernhard
I am a math hobbyist working through John Stillwell's book "Elements of Number Theory"

On page 3 Stillwell after pointing out that $\displaystyle n^2 +n + 41$ is prime for all small values of n, poses the following problem:

"Show, nevertheless that $\displaystyle n^2 +n + 41$ is not prime for certain values of n"

Can anyone help me with this problem? I would certainly like to see a rigorous proof.

Simple: take $\displaystyle n=41$...

Tonio

3. Originally Posted by Bernhard
I am a math hobbyist working through John Stillwell's book "Elements of Number Theory"

On page 3 Stillwell after pointing out that $\displaystyle n^2 +n + 41$ is prime for all small values of n, poses the following problem:

"Show, nevertheless that $\displaystyle n^2 +n + 41$ is not prime for certain values of n"

Can anyone help me with this problem? I would certainly like to see a rigorous proof.
Can you show that the expression can produce numbers ending in 5 for certain values of n? (except for 5 itself obviously).

4. Thanks Tonio

Certainly was simple ... I supoose also that a demonstration like that is a rigourous proof.

Bernhard

5. Originally Posted by Bernhard
Thanks Tonio

Certainly was simple ... I supoose also that a demonstration like that is a rigourous proof.

Bernhard
For proving an object exists, it is sufficient to produce such an object.

Likewise, for proving a statement is false, it is sufficient to produce a counterexample.

So, yes, it is rigorous.