Count the number of prime numbers less than N
A prime number (prime number) is also called a prime number, which is a natural number greater than 1 and has no other factors except 1 and itself. The opposite is a composite number, and there are infinite prime numbers.
Count the number of prime numbers less than N
输入: 10输出: 4
There are 4 prime numbers less than 10: 2, 3, 5, 7
Method 1: Direct Judgment
from math import sqrt
def isPrime(n):
for i in range(2,int(sqrt(n))+1):
if n%i==0:
return False
return True
def countPrime(N):
if N<3:
return 0
else:
cou = 1
for i in range(3,N,2):
if isPrime(i):
cou += 1
return cou
print(countPrime(2))
print(countPrime(5))
print(countPrime(100))
print(countPrime(100000))
print(countPrime(10000000))#在n>100000000时达到计算瓶颈
Output:
0
2
25
9592
664579
Method 2: Elsieve sieve method
The Sieve of Eratosthenes, referred to as the Sieve of Eratosthenes, is a screening method proposed by the ancient Greek mathematician Eratosthenes (Eratosthenes 274BC.～194BC.).
To get all the prime numbers within the natural number n, the multiples of all prime numbers not greater than n must be removed, and the rest are prime numbers. The specific steps are as follows: first use 2 to sieve, that is, keep 2, and remove the multiples of 2; Then use the next prime number, that is, 3 to sieve, keep 3, and remove multiples of 3; then use the next prime number 5 to sieve, keep 5, and remove multiples of 5; repeat.
def couPrime(N):
primeList = [True]*N
for i in range(2,N):
if(primeList[i]):
for j in range(2*i,N,i):
primeList[j]=False
cou = primeList.count(True)-2
return cou
print(couPrime(100000000)) #在n>1000000000达到计算瓶颈
Output:
5761455