Question

If p and 8p - 1 are prime numbers. Prove that 8p isn't a prime number.​

Answer 1

Answer:

Since 8P-1 is prime, it is not divisible by 3 either. Since we cannot have three successive numbers that are not divisible by 3, that means 8P+1 must be divisible by 3, and hence composite. That just leaves the case P = 3, but then 8P-1 is 23 and 8P+1 is 25, which is composite. Thus the statement is true.