1. ## 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

2. 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: $\displaystyle a^3+b^3 = (a+b)(a^2 - ab + b^2)$

3. 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.

4. 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 $\displaystyle n^3+1$ as a product of two integers.
So how can it be prime?

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

6. Originally Posted by rmpatel5
so anything that factors can not be prime because that makes it a composite?
Yes if $\displaystyle a = bc$ and neither $\displaystyle b,c$ are $\displaystyle 1$ then $\displaystyle a$ cannot be prime.