prove that 37 is prime

Question : prove that 37 is prime.

Solution :

To prove 37 is prime.

We know that if n>1 is composite then n has a prime divisor p that satisfies

\[p\le\sqrt{n}\]

Since 49 is composite so all the prime divisors of 49 satisfies

\[p\le\sqrt{49}=7\]

The primes less than 7 are 2, 3, 5. Since none of these divides 37.

 So 37 is prime.