If p is a prime integer then p + 19 is composite. I thinks this is true but I have no way of proving this.?

All primes, other than 2, are odd. They can be expressed as 2k + 1, where k is an integer

2k + 1 + 19 =>

2k + 20 =>

2 * (k + 10)

If p = 2, then we have

2 + 19 = 21 = 3 * 7

True.

The only even prime is "2". p + 19 in this case is 21, a composite number.

All other primes are odd. Add 19 to an odd number, you'll get an even number. All even integers greater than 2 are always composite.

An odd number plus an odd number equals an even number, and 2 is the only even prime (because all other even numbers are divisible by 2).