Divide 97 by 2. This will be your baseline.
$${\frac{{\mathtt{97}}}{{\mathtt{2}}}} = {\mathtt{48.5}}$$
Now, start by dividing 97 by each succesive prime number.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41 , 43, 47
Skip 3 because 9 + 7 which is not a multiple of 3.
Skip 5 because 97 does not end in 5.
$${\frac{{\mathtt{97}}}{{\mathtt{7}}}} = {\mathtt{13.857\: \!142\: \!857\: \!142\: \!857\: \!1}}$$
$${\frac{{\mathtt{97}}}{{\mathtt{11}}}} = {\mathtt{8.818\: \!181\: \!818\: \!181\: \!818\: \!2}}$$
$${\frac{{\mathtt{97}}}{{\mathtt{13}}}} = {\mathtt{7.461\: \!538\: \!461\: \!538\: \!461\: \!5}}$$
We already know that no prime number below 7 works, because the quotient of 97/13 is 7 and there are no prime numbers less than 7 that will work. So we can conclude that 97 is indeed prime.
Divide 97 by 2. This will be your baseline.
$${\frac{{\mathtt{97}}}{{\mathtt{2}}}} = {\mathtt{48.5}}$$
Now, start by dividing 97 by each succesive prime number.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41 , 43, 47
Skip 3 because 9 + 7 which is not a multiple of 3.
Skip 5 because 97 does not end in 5.
$${\frac{{\mathtt{97}}}{{\mathtt{7}}}} = {\mathtt{13.857\: \!142\: \!857\: \!142\: \!857\: \!1}}$$
$${\frac{{\mathtt{97}}}{{\mathtt{11}}}} = {\mathtt{8.818\: \!181\: \!818\: \!181\: \!818\: \!2}}$$
$${\frac{{\mathtt{97}}}{{\mathtt{13}}}} = {\mathtt{7.461\: \!538\: \!461\: \!538\: \!461\: \!5}}$$
We already know that no prime number below 7 works, because the quotient of 97/13 is 7 and there are no prime numbers less than 7 that will work. So we can conclude that 97 is indeed prime.
