List of prime numbers to 503/21/2024 ![]() Instead of trial division, a better approach, invented by the Greek mathematician Eratosthenes over two thousand years ago, is to sieve by repeatedly casting out multiples of primes.īegin by making a list of all numbers from 2 to the maximum desired prime n. ![]() Need to check with even numbers, so 'i' value can be start with 3 and Like so: import mathĪs in the first loop odd numbers are selected, in the second loop no You can improve it a little more by incrementing the range you check by 2, and thereby only checking odd numbers. If all(num%i!=0 for i in range(2,int(math.sqrt(num))+1)):įor small numbers like 101 it doesn't matter, but for 10**8 the difference will be really big. You can write the same much shorter and more pythonic: for num in range(2,101):Īs I've said already, it would be better to check divisors not from 2 to n-1, but from 2 to sqrt(n): import math ![]() If n is divisible by any of the numbers, it is not prime. You need to check all numbers from 2 to n-1 (to sqrt(n) actually, but ok, let it be n). ![]()
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