# Simple prime number generator in Python

## Simple prime number generator in Python

There are some problems:

- Why do you print out count when it didnt divide by x? It doesnt mean its prime, it means only that this particular x doesnt divide it
`continue`

moves to the next loop iteration – but you really want to stop it using`break`

Heres your code with a few fixes, it prints out only primes:

```
import math
def main():
count = 3
while True:
isprime = True
for x in range(2, int(math.sqrt(count) + 1)):
if count % x == 0:
isprime = False
break
if isprime:
print count
count += 1
```

For much more efficient prime generation, see the Sieve of Eratosthenes, as others have suggested. Heres a nice, optimized implementation with many comments:

```
# Sieve of Eratosthenes
# Code by David Eppstein, UC Irvine, 28 Feb 2002
# http://code.activestate.com/recipes/117119/
def gen_primes():
Generate an infinite sequence of prime numbers.
# Maps composites to primes witnessing their compositeness.
# This is memory efficient, as the sieve is not run forward
# indefinitely, but only as long as required by the current
# number being tested.
#
D = {}
# The running integer thats checked for primeness
q = 2
while True:
if q not in D:
# q is a new prime.
# Yield it and mark its first multiple that isnt
# already marked in previous iterations
#
yield q
D[q * q] = [q]
else:
# q is composite. D[q] is the list of primes that
# divide it. Since weve reached q, we no longer
# need it in the map, but well mark the next
# multiples of its witnesses to prepare for larger
# numbers
#
for p in D[q]:
D.setdefault(p + q, []).append(p)
del D[q]
q += 1
```

Note that it returns a generator.

re is powerful:

```
import re
def isprime(n):
return re.compile(r^1?$|^(11+)1+$).match(1 * n) is None
print [x for x in range(100) if isprime(x)]
###########Output#############
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
```

#### Simple prime number generator in Python

```
def is_prime(num):
Returns True if the number is prime
else False.
if num == 0 or num == 1:
return False
for x in range(2, num):
if num % x == 0:
return False
else:
return True
>> filter(is_prime, range(1, 20))
[2, 3, 5, 7, 11, 13, 17, 19]
```

We will get all the prime numbers upto 20 in a list.

I could have used Sieve of Eratosthenes but you said

you want something very simple. 😉