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)
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?
then 41^2 + 41 + 41=1763
it still prime!!!!
No, it is obviously divisible by 41.
It's an easy exercise to show that no polynomial with integer coefficients yields only primes.
It must surely be the only composite prime number, then. ; )
Originally Posted by lebanon
There aren't very many of them, I've heard!