Python Prime Checker Algorithm
Check if a number is prime using Python. Run our interactive algorithm to see efficient mathematical iteration and root evaluation.
How it Works
A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself.
The most inefficient way to check for a prime is iterating up to the number itself. A powerful optimization is to only check divisibility up to the square root of the number.
Source Code
Efficient prime checking algorithm demonstrating the O(sqrt(n)) optimization.
import math
def is_prime(n):
if n <= 1:
return False
if n == 2:
return True
if n % 2 == 0:
return False
max_divisor = math.isqrt(n)
for i in range(3, max_divisor + 1, 2):
if n % i == 0:
return False
return True
test_numbers = [2, 10, 17, 25, 97]
for num in test_numbers:
status = "Prime" if is_prime(num) else "Not Prime"
print(f"{num:2d} -> {status}") 2 -> Prime
10 -> Not Prime
17 -> Prime
25 -> Not Prime
97 -> PrimeReal-world Applications
- Cryptography and hashing algorithms
- Educational mathematics and sieve theory
- Backend validation for secure keys
Frequently Asked Questions
Why check only up to the square root?
If $n = a \times b$, then at least one of the factors ($a$ or $b$) must be less than or equal to the square root of $n$. Thus, checking higher is redundant.
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