Compute p200200ln200Solution200 is not a large number so we

Compute p(200)/(200/ln(200)).

Solution

200 is not a large number so we compute p(200) by literally counting all primes less than equal to 200. There is no known exact formula for this. Only asymptotic formulas are there. But for a small number we can compute exactly.

All the primes less than 200 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

These are:

46 in number.

Hence, p(200)=46

200/ln(200)=37.7478

Hence, p(200)/(200/ln(200))=1.2186