# n^2 + n + 41 and primes

• Jan 26th 2010, 07:49 AM
lebanon
n^2 + n + 41 and primes
consider the relation n^2 + n + 41
one person claim that this relation does not apply for primes:
for n=1 it gives 43 : its prime
for n=2 it gives 47:its prime
for n=3 it gives 53 : its prime;etc...
Does this man have a reason for his claim?(Headbang)
• Jan 26th 2010, 07:56 AM
Manx
old favorite
This problem is often used to help students see the importance of mathematical proof. If you try many values of n, the expression yields a prime. Can we therefore assume that it will ALWAYS yield a prime?

What happens if n=41?
• Jan 26th 2010, 08:01 AM
lebanon
if n=41
then 41^2 + 41 + 41=1763
it still prime!!!!
• Jan 26th 2010, 08:03 AM
Bruno J.
No, it is obviously divisible by 41.

It's an easy exercise to show that no polynomial with integer coefficients yields only primes.
• Jan 26th 2010, 08:03 AM
hatsoff
Quote:

Originally Posted by lebanon
if n=41
then 41^2 + 41 + 41=1763=43*41
it still prime!!!!

It must surely be the only composite prime number, then. ; )
• Jan 26th 2010, 08:13 AM
Manx
There aren't very many of them, I've heard!