light_primes.py

from Crypto.Util.number import isPrime
import math
import time

primes = []

def find_primes(max_val):
    N = math.ceil(math.sqrt(max_val))
    for n in range(0,N,2):
        p = n**2 + 1
        if isPrime(p):
            primes.append((p,n))
    return primes

max_value = 100_000_000
t_start = time.time()
primes = find_primes(max_value)
t_end = time.time()

print(f"Time taken: {round(t_end - t_start, 5)}s")

p,n = primes[-1]
print(f"Max value found: {p} = {n}^2 + 1")
print(f"Total primes for n <= {max_value}: {len(primes)}")

# Time taken: 0.70909s
# Max value found: 99800101 = 9990^2 + 1
# Total primes n^2 + 1 <= 100000000: 840