Python Challenges: Find the 1000th prime number

Last update on December 21 2024 07:49:39 (UTC/GMT +8 hours)

Write a python program to find the 1000th prime number.

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes. The first twenty prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.

Sample Solution:

Python Code:

def eratosthenes():
    D = {}  
    q = 2   
    while 1:
        if q not in D:
            yield q        
            D[q*q] = [q]   
        else:
            for p in D[q]: 
                D.setdefault(p+q,[]).append(p)
            del D[q]       
        q += 1

def nth_prime(n):
    for i, prime in enumerate(eratosthenes()):
        if i == n - 1:
            return prime

print(nth_prime(1000))

Sample Output:

Flowchart:

Python Code Editor:

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