James says that if prime number is doubled, then that new number is still a prime number
State whether you agree or disagree, and explain why you think so (e.g. you may refer to a definition). If you agree, give an example that proves James conjecture. If you disagree, give a counterexample that disproves James conjecture
I disagree with James' conjecture.
To explain why, let's first recall the definition of a prime number - a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Now, if we consider doubling a prime number, let's say p, then the new number would be 2p. To disprove James' conjecture, I need to find a counterexample where 2p is not a prime number.
One such counterexample is when p = 3, a prime number. If we double 3, we get 2p = 2 * 3 = 6, which is not a prime number since it has divisors other than 1 and itself (2 and 3). Therefore, the counterexample of 2p = 6 disproves James' conjecture.
In conclusion, doubling a prime number does not necessarily result in a prime number, as demonstrated by the counterexample of p = 3.