If you add one to a prime number, it will yield another prime number.
what would be a counterexample?
would it be 2?
3 + 1 = 4
3 would be possible?
thank you!
In fact, that statement is easily proven false for all primes except 2.
All the other primes are odd. Adding 1 will give an even result, which, as a multiple of 2, cannot be prime.
so, would 0 be a possibility?
No. zero is not a prime.
Review the definition of a prime. It is a positive integer other than 1, with no other factors besides 1 and itself.
0 is not only not positive, it has many "factors," since for any number x,
x*0 = 0
To determine if adding one to a prime number always yields another prime number, we can examine the definition of a prime number. A prime number is a natural number greater than 1 that has no divisors other than 1 and itself.
The number 2 is the only even prime number, and it is a special case because it is the only even number that is prime. Adding 1 to 2 gives us 3, which is indeed a prime number.
However, a counterexample to the statement "If you add one to a prime number, it will yield another prime number" is 3. Adding 1 to 3 gives us 4, which is not a prime number. Therefore, 3 is a counterexample to the statement.
In conclusion, the counterexample to the statement "If you add one to a prime number, it will yield another prime number" is 3.