```
''' timeit_isprime.py
check the speed of five isprime functions
tested with Python34 by vegaseat (dns) 16may2015
'''
import timeit
import sys
print(sys.version)
def isprime2(n):
'''
check if integer n is a prime, return True or False
'''
# 2 is the only even prime
if n == 2:
return True
# integers less than 2 and even numbers other than 2 are not prime
elif n < 2 or not n & 1:
return False
#if n % 3 == 0: return False
# loop looks at odd numbers 3, 5, 7, ... to sqrt(n)
for i in range(3, int(n**0.5)+1, 2):
if n % i == 0:
return False
return True
def isprime3(n):
'''
check if integer n is a prime, return True or False
'''
# 2 is the only even prime
if n == 2:
return True
# integers less than 2 and even numbers other than 2 are not prime
if n < 2:
return False
if not n & 1: # even numbers
return False
# loop looks at odd numbers 3, 5, 7, ... to sqrt(n)
for i in range(3, int(n**0.5)+1, 2):
if n % i == 0:
return False
return True
def isprime4(n):
'''
check if integer n is a prime, return True or False
uses a while loop, another way to write it, but is slower
'''
# 2 is the only even prime
if n == 2:
return True
# integers less than 2 and even numbers other than 2 are not prime
if n < 2:
return False
if n % 2 == 0: # even numbers
return False
k = 3
while k * k <= n:
if n % k == 0:
return False
k += 2
return True
def isprime5(n):
# deal with low primes and even numbers
if n in (2,3,5,7,): return True
if n < 2 or n%2 == 0: return False
if n%3 == 0: return False
# need divisors only up to sqrt(x) or n**0.5
sqr = int(n**0.5)
div = 5
while div <= sqr:
if n%div == 0: return False
if n%(div+2) == 0: return False
# loop every 6th integer
div += 6
return True
def isprime6(n):
# no negative numbers
n = abs(n)
# deal with primes under 5
if n in (2,3,):
return True
# the rest of the primes are multiples of 6 plus or minus 1
# this eliminate 2/3 of the remaining candidates
if (n < 5) or ((n % 6) not in (1, 5,)):
return False
# need divisors only up to math.sqrt(x)+2 (same as n**0.5+2)
for div in range(6, int(n**0.5+2), 6):
if (n % (div+1) == 0) or (n % (div-1) == 0):
return False
return True
# note 9999991 is a prime number, use for testing
print("isprime2(9999991) = {}".format(isprime2(9999991)))
print("isprime3(9999991) = {}".format(isprime3(9999991)))
print("isprime4(9999991) = {}".format(isprime4(9999991)))
print("isprime5(9999991) = {}".format(isprime5(9999991)))
print("isprime6(9999991) = {}".format(isprime6(9999991)))
stmt = 'isprime2(9999991)'
find_function = 'from __main__ import isprime2'
t = timeit.Timer(stmt, setup=find_function)
# doing 1000 passes * 1000 gives the time in microseconds/pass
elapsed = (1000 * t.timeit(number=1000))
print("%s takes %0.3f micro-seconds/pass" % (stmt, elapsed))
stmt = 'isprime3(9999991)'
find_function = 'from __main__ import isprime3'
t = timeit.Timer(stmt, setup=find_function)
# doing 1000 passes * 1000 gives the time in microseconds/pass
elapsed = (1000 * t.timeit(number=1000))
print("%s takes %0.3f micro-seconds/pass" % (stmt, elapsed))
stmt = 'isprime4(9999991)'
find_function = 'from __main__ import isprime4'
t = timeit.Timer(stmt, setup=find_function)
# doing 1000 passes * 1000 gives the time in microseconds/pass
elapsed = (1000 * t.timeit(number=1000))
print("%s takes %0.3f micro-seconds/pass" % (stmt, elapsed))
stmt = 'isprime5(9999991)'
find_function = 'from __main__ import isprime5'
t = timeit.Timer(stmt, setup=find_function)
# doing 1000 passes * 1000 gives the time in microseconds/pass
elapsed = (1000 * t.timeit(number=1000))
print("%s takes %0.3f micro-seconds/pass" % (stmt, elapsed))
stmt = 'isprime6(9999991)'
find_function = 'from __main__ import isprime6'
t = timeit.Timer(stmt, setup=find_function)
# doing 1000 passes * 1000 gives the time in microseconds/pass
elapsed = (1000 * t.timeit(number=1000))
print("%s takes %0.3f micro-seconds/pass" % (stmt, elapsed))
''' result ...
3.4.2 |Continuum Analytics, Inc.| (default, Oct 21 2014, 17:42:20)
[GCC 4.2.1 (Apple Inc. build 5577)]
isprime2(9999991) = True
isprime3(9999991) = True
isprime4(9999991) = True
isprime5(9999991) = True
isprime6(9999991) = True
isprime2(9999991) takes 162.309 micro-seconds/pass
isprime3(9999991) takes 162.340 micro-seconds/pass
isprime4(9999991) takes 280.765 micro-seconds/pass
isprime5(9999991) takes 135.013 micro-seconds/pass
isprime6(9999991) takes 127.583 micro-seconds/pass
'''
```

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