Added fermat_test.md

snippets/fermat_test.md

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+### fermat_test
+
+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. Appling 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.
+
+``` python
+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
+
+```
+
+``` python
+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
+```