To find first N prime numbers in python

Question

I am new to the programming world. I was just writing this code in python to generate N prime numbers. User should input the value for N which is the total number of prime n

Answer 1

Whilst playing with prime numbers in Python V3 I noticed that the smallest number by which a composite(non-prime) number is divisible is itself always a prime that is less than the square root of the number under test.

Below is my implementation of that finding to calculate the first N prime numbers.

first 1,000 primes in 0.028S | first 10,000 primes in 0.6S | first 100,000 primes in 14.3S

The snippet below also indicates how long the generation took and prints out the primes in a nice table format.

import time
import math

def first_n_Primes(n):
    number_under_test = 4
    primes = [2,3]
    while len(primes) < n:
        check = False
        for prime in primes:
            if prime > math.sqrt(number_under_test) : break
            if number_under_test % prime == 0:
                check = True
                break
        if not check:
            for counter in range(primes[len(primes)-1],number_under_test-1,2):
                if number_under_test % counter == 0:
                    check = True
                    break
        if not check:
            primes.append(number_under_test)
        number_under_test+=1
    return primes

start_time = time.time()
data = first_n_Primes(1000)
end_time = time.time()

i = 1
while i < len(data)+1:
    print('{0: <9}'.format(str(data[i-1])), end="")
    if i%10 == 0: print("")
    i+=1

print("\nFirst %d primes took %s seconds ---" % (len(data),end_time - start_time))