def main():
diff = 3330
seen = set([1487, 4817, 8147])
primeset = set(primes(10000))
for p in primes(10000):
if (p < (1000 + diff)) or ('0' in str(p)) or (p in seen):
continue
if (p - diff) in primeset and (p + diff) in primeset:
if is_permutation(p, p - diff) and is_permutation(p, p + diff):
return ''.join(map(str, [p - diff, p, p + diff]))
return None
def euler_35():
"""How many circular primes are there below one million?"""
from itertools import takewhile
from eutil import primes, rotations
ps = set(takewhile(lambda p: p < 1000000, primes()))
return len(filter(None, [all((x in ps) for x in [int(r) for r in rotations(str(p))]) for p in ps]))
def euler_3():
"""Find the largest prime factor of a composite number."""
from math import sqrt
from itertools import takewhile
from eutil import primes
num = 600851475143
ps = takewhile(lambda p: p < sqrt(num), primes())
return max([p for p in ps if num % p == 0])
def euler_69():
"""Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum."""
from eutil import primes
n = 1
for p in primes():
if (n * p) > 1000000:
break
n = n * p
return n
def euler_26():
"Find the value of d < 1000 for which 1/d contains the longest recurring cycle."
from itertools import count, dropwhile, takewhile
from eutil import primes
ps = list(takewhile(lambda x: x < 1000, primes()))
for p in reversed(ps):
c = next(dropwhile(lambda x: (pow(10, x) - 1) % p != 0, count(start=1)))
if p - c == 1:
return p
def euler_27():
"Find a quadratic formula that produces the maximum number of primes for consecutive values of n."
from itertools import chain, imap, product, takewhile, tee
from eutil import ilen, primes, is_prime, sequence
a_s = xrange(-999, 1000)
ps = tee(takewhile(lambda p: p < 1000, primes()))
b_s = chain(ps[0], imap(lambda x: -x, ps[1]))
seqs = [(ilen(takewhile(is_prime, sequence(lambda n: n ** 2 + a * n + b))), a, b) for a, b in product(a_s, b_s)]
seq = max(seqs, key=lambda t: t[0])
return seq[1] * seq[2]
def main():
n = 1000000
primelist = primes(5000)
longest = []
for i in range(len(primelist)):
for j in range(i + len(longest), len(primelist)):
if sum(primelist[i:j]) > n:
break
if (j - i) > len(longest):
if is_prime(sum(primelist[i:j])):
longest = primelist[i:j]
return len(longest), sum(longest)
def main():
n = 1000000
primelist = primes(5000)
longest = []
for i in range(len(primelist)):
for j in range(i + len(longest), len(primelist)):
if sum(primelist[i:j]) > n:
break
if (j - i) > len(longest):
if is_prime(sum(primelist[i:j])):
longest = primelist[i:j]
return len(longest), sum(longest)
def euler_10():
"""Calculate the sum of all the primes below two million."""
from itertools import takewhile
from eutil import primes
return sum(takewhile(lambda p: p < 2000000, primes()))
