Then n is called a prime number if n has exactly two positive divisors, 1 and n. Then q is also a prime divisor of n and q < m < \sqrt{n} < p. This is a contradiction. B...Then n is called a prime number if n has exactly two positive divisors, 1 and n. Then q is also a prime divisor of n and q < m < \sqrt{n} < p. This is a contradiction. But this is impossible since there is no prime that divides 1 and as a result q is not one of the primes listed. Consider the sequence of integers (n+1)!+2, (n+1)!+3,...,(n+1)!+n, (n+1)!+(n+1)
