def main():
# based on Fermat's Little Theorem
r = 0
for p in take_while(primes(), lambda p: p < 1000):
if p == 2 or p == 5: continue
rp = multiplicative_order(10, p)
if rp > r:
r = rp
q = p
return q
from funcs import primes
from math import sqrt
num = 600851475143
for p in primes( int(sqrt(num)+2) )[::-1]:
if num%p == 0:
print p
break
def main():
gen = primes()
for i in range(10001):
p = next(gen)
return p
def main():
return sum(take_while(primes(), lambda p: p < 2000000))
from funcs import count_divisors, primes
t = 0
i = 0
plist = primes( 10**4, 500 )
max_divs = 0
while True:
i += 1
t += i
n_div = count_divisors( t, plist )
if n_div > max_divs:
print "{0} has {1} divisors".format( t, n_div )
max_divs = n_div
if n_div > 500:
break
print t
from funcs import primes print primes(10**6,10001)[10000]
from operator import mul
from funcs import primes
stride=reduce( mul, primes(20) )
n = stride
while True:
is_div = True;
for i in range(1,21):
if n % i != 0:
is_div = False
break
if is_div:
break
n += stride
print n
from funcs import primes print sum( primes( 2*10**6 - 1 ) )
def test_find_up_to_0(self):
self.assertEqual(list(primes(0)), [])
def test_find_up_to_ten(self):
self.assertEqual(list(primes(10)), [2, 3, 5, 7])
from funcs import primes, get_abundant_numbers
plist = primes( 10**5 )
abunds = get_abundant_numbers( 2, 30000, plist )
def sum_of_2_abunds( n ):
a = 0
z = len(abunds) - 1
while a <= z:
cand = abunds[a] + abunds[z]
if cand == n:
return (abunds[a],abunds[z])
elif cand < n:
a += 1
else:
z -= 1
return None
tot = 0
for i in range(1, 28123):
if sum_of_2_abunds(i) == None:
tot += i
print tot