10001st Prime#

package main

import (
    "fmt"
    "math/big"
)

func firstNPrime(n int) int {
    var nPrime int = 0

    for i := 2; n != 0; i++ {
        if big.NewInt(int64(i)).ProbablyPrime(0) {
            nPrime = i
            n--
        }
    }

    return nPrime
}

func main() {
    fmt.Println(firstNPrime(10001))
}

OUTPUT

104743

Python Solutions by Yogisam72#

Solution 1#

import time

prime = [2]
index = 10001
prime_numbers_array_length = 1


t0 = time.time() 

i = 3
while prime_numbers_array_length != index:

    flag = 1

    for j in prime[:round(prime_numbers_array_length**0.5)]:
        if i%j == 0:
            flag = 0
            break

    if flag == 1:
        prime.append(i)

    prime_numbers_array_length = len(prime)

    i += 2

print("10001st prime number is:",prime[-1])

t1 = time.time() 
print("Time required:", t1 - t0) 

OUTPUT

10001st prime number is: 104743
Time required: 0.1237955093383789

Solution 2#

import time 
def SieveOfEratosthenes(n): 

    prime = [True for i in range(n+1)] 
    prime_numbers=[]

    p = 2
    while(p * p <= n): 

        # If prime[p] is not changed, then it is  
        # a prime.
        if (prime[p] == True): 

            # Update all multiples of p 
            for i in range(p * p, n + 1, p): 
                prime[i] = False
        p += 1


    # Print all prime numbers 
    for p in range(2, n): 
        if prime[p]: 
            prime_numbers.append(p)


    return prime_numbers[10000]



t0 = time.time() 
c = SieveOfEratosthenes(110000) 
print("10001st prime number is:", c) 

t1 = time.time() 
print("Time required:", t1 - t0) 

OUTPUT:

10001st prime number is: 104743
Time required: 0.021940946578979492