# Integer - Prime Number

A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself.

All prime numbers are Integer - Parity (Even|Odd), with one exception: the prime number 2.

## Python Function

### Naive way

``````def is_prime(x):
if x > 1:
for i in range(2,x-1):
if (x % i == 0):
return False
else:
return False
return True```
```

### Second

Python script that gives false positives when input is a Carmichael number (rare) and otherwise with probability 1/20

``````from random import randint
def is_prime(p, n=20): return all([pow(randint(1,p-1),p-1,p) == 1 for i in range(n)])

for i in range(2,10):
print(i,is_prime(i))```
```
``````2 True
3 True
4 False
5 True
6 False
7 True
8 False
9 False
```
```

Recommended Pages Mathematics - (Prime Factorization Theorem | Factoring integers)

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