204. Count prime numbers

Count All integers smaller than non-negative integersNNumber of prime numbers.

Example:

Input: 10 output: 4 explanation: There are four prime numbers smaller than 10, which are 2, 3, 5, and 7.

/* Int countprimes (int n) {int COUNT = 0; If (n = 0 | n = 1) return 0; For (Int J = 2; j <= N; j ++) {If (isprime (j) Count ++;} return count;}/* bool isprime (int n) {If (n <2) return false; For (INT I = 2; I * I <= N; I ++) {If (N % I = 0) return false;} return true;} * // * bool isprime (INT num) {If (Num <= 3) {return 2 ;} // If (Num % 6! = 1 & num % 6! = 5) {return false;} For (INT I = 5; I * I <num; I + = 6) {If (Num % I = 0 | num % (I + 2) = 0) {return false ;}} return true ;}*/INT countprimes (INT N) {int sum = 0; If (n = 0 | n = 1) return 0; For (INT I = 2; I <n; I ++) {If (isprime (I) sum ++;} return sum;} bool isprime (INT num) {If (num = 2 | num = 3) return true; // If (Num % 6! = 1 & num % 6! = 5) return false; int TMP = SQRT (Num); // either of the multiples of 6 May not be a prime number for (INT I = 5; I <= TMP; I + = 6) if (Num % I = 0 | num % (I + 2) = 0) return false; // exclude all, the remainder is the prime number return true ;}

/* For further analysis, another feature of prime number is that it is always 6 x-1 or 6 x + 1, where X is a natural number greater than or equal to 1.

It is not difficult to prove this conclusion. First, 6x is definitely not a prime number, because it can be divisible by 6; secondly, 6x + 2 is certainly not a prime number, because it can also be divisible by 2; and so on, 6x + 3 can certainly be divided by 3; 6x + 4 can certainly be divided by 2. Then, only 6x + 1 and 6X + 5 (equivalent to 6x-1) may be prime numbers. So the cycle step can be set to 6, and then only the number of the six sides can be determined at a time. */

 

204. Count prime numbers