Hello,
10*10=100>89
n=89 is prime if it not divisible by all prime less then its square root
0<89<100 ==>0<√89<10
The primes to test are 2,3,5,7.
89 does not end with a even digit ==> 89 is not divisible by 2
8+9=17 if not divisible by 3 ==>89 is not divisible by 3
89 does not end with 0 or 5 ==>89 is not divisible by 5
3*8+1*9=33 is not divisible by 7 ==>89 is not divisible by 7
So: 89 is prime.