36 lines
966 B
Markdown
36 lines
966 B
Markdown
---
|
|
title: fermat_test
|
|
tags: math
|
|
---
|
|
Checks if the number is prime or not. Returns True if passed number is prime, and False if not.
|
|
|
|
The function uses Fermat's theorem.
|
|
First, it picks the number `A` in range `1`..`(n-1)`, then it checks if `A` to the power of `n-1` modulo `n` equals `1`.
|
|
If not, the number is not prime, else it's pseudoprime with probability 1/2. Applying this test `k `times we have probability `1/(2^k)`.
|
|
For example, if the number passes the test `10` times, we have probability `0.00098`.
|
|
|
|
```py
|
|
from random import randint
|
|
|
|
|
|
def fermat_test(n, k=100):
|
|
if n <= 1:
|
|
return False
|
|
for i in range(k):
|
|
a = randint(1, n - 1)
|
|
if pow(a, n - 1, n) != 1:
|
|
return False
|
|
return True
|
|
|
|
```
|
|
|
|
```py
|
|
fermat_test(0) # False
|
|
fermat_test(1) # False
|
|
fermat_test(561) # False
|
|
fermat_test(41041) # False
|
|
fermat_test(17) # True
|
|
fermat_test(162259276829213363391578010288127) # True
|
|
fermat_test(-1) # False
|
|
```
|