check less n primes (good, better methods)

check_prime.py

import math


def tri_prime(n):
    primes = [2]

    def is_prime(number):
        if number % 2 == 0: return False
        for i in range(3, math.floor(number / 2) + 1):
            if number % i == 0:
                return False
        return True

    for i in range(3, n + 1):
        if is_prime(i):
            primes.append(i)
    return primes


def good_prime(n):
    primes = [2]

    def is_prime(number):
        if number % 2 == 0 and n > 2:
            return False
        return all(number % i for i in range(3, int(math.sqrt(number)) + 1, 2))

    for i in range(3, n + 1):
        if is_prime(i):
            primes.append(i)
    return primes


def better_prime(n):
    primes = [2]

    def is_prime(number):
        if number % 2 == 0: return False
        sqrt_n = int(math.sqrt(number))
        for p in primes:
            if p > sqrt_n: return True
            if number % p == 0: return False

        if sqrt_n <= primes[-1]:
            return True
        elif sqrt_n > primes[-1]:
            # almost do not
            return all(number % j for j in range(primes[-1], sqrt_n + 1, 2))

    for i in range(3, n + 1):
        if is_prime(i):
            primes.append(i)
    return primes

def odd_prime(n):
    primes = [2, 3]

    def is_prime(number):
        if number % 2 == 0 or number % 3 == 0: return False
        x = int((number - 3) / 2)
        y = 1
        for i in range(x, 1, -3):
            if i >= y:
                if y != 1 and i % y == 0:
                    return False
            else:
                break
            y += 2
        return True

    for i in range(5, n + 1):
        if is_prime(i):
            primes.append(i)
    return primes