Thread: prime number conjecture

disprove the conjecture: There are infinitely many prime numbers expressible in the form n^3 +1 where n is a positive integer

Originally Posted by rmpatel5

disprove the conjecture: There are infinitely many prime numbers expressible in the form n^3 +1 where n is a positive integer

Hint:

I have that part: n^3 +1= (n+1)(n^2-n+1). Just dont know where to go from. I know that 2 is the only integer that will work but i just dont know how to prove it.

Originally Posted by rmpatel5

I have that part: n^3 +1= (n+1)(n^2-n+1). Just dont know where to go from. I know that 2 is the only integer that will work but i just dont know how to prove it.

Well because you can factor as a product of two integers.
So how can it be prime?

so anything that factors can not be prime because that makes it a composite?

Originally Posted by rmpatel5

so anything that factors can not be prime because that makes it a composite?

Yes if and neither are then cannot be prime.