"""
from math import log10
from bisect import bisect_left
from utils.primes import load_primes
def num_digits(n):
return int(log10(n)) + 1
def rotate(n):
return n % 10 * 10**int(log10(n)) + n / 10
primes = load_primes()
primes = primes[bisect_left(primes, 100):bisect_left(primes, 1000000)]
prime_set = set(primes)
count = 13
while len(prime_set) > 0:
n = prime_set.pop()
for i in xrange(num_digits(n) - 1):
n = rotate(n)
if n not in prime_set:
break
prime_set.remove(n)
else:
count += num_digits(n)
print count
# Author: Deddryk """ Solution for problem 10. This was simple using the utils.primes module written for problem 3. """ from utils.primes import load_primes print sum(load_primes())
Solution to problem 37
"""
from bisect import bisect_left
from math import log10
from utils.primes import load_primes
def truncate_left(n):
return n % 10**(int(log10(n)))
def truncate_right(n):
return n / 10
primes = load_primes()
primes_set = set(primes)
num_truncatable_primes = 0
truncatable_primes_sum = 0
for prime in primes[bisect_left(primes, 10):]:
if num_truncatable_primes == 11:
break
truncl, truncr = truncate_left(prime), truncate_right(prime)
while truncl != 0 and truncr != 0:
if truncl not in primes_set or truncr not in primes_set:
break
truncl = truncate_left(truncl)
truncr = truncate_right(truncr)
else:
print prime
num_truncatable_primes += 1
"""
Solution to problem 27
Essentially this solution loops through every possible coefficient
a and b and checks to see how many primes are generated for consecutive
n starting at 0. Some time is saved by using only primes for b since
for the case n = 0, b must be prime. It uses the utils.primes module
for prime generation and slices the generated list to all primes < 1000,
then makes a set for fast in checks.
"""
from utils.primes import load_primes
primes = set(load_primes())
small_primes = [x for x in primes if x < 1000]
def count_primes(a, b):
count = 1
n = 1
while n*n + a*n + b in primes:
count += 1
n += 1
return count
most = (40, 1, 41)
for a in xrange(-999, 1000):
for b in small_primes:
primes_gen = count_primes(a, b)
if primes_gen > most[0]: