#!/usr/bin/env python
from math_tools import is_prime
"""https://projecteuler.net/problem=3"""
if __name__ == '__main__':
cmp = 600851475143
print(
next(div for div in xrange(int(cmp**0.5), 1, -1)
if cmp % div == 0 and is_prime(div)))
#!/usr/bin/env python
from math_tools import rotations, primes, is_prime
"""https://projecteuler.net/problem=35"""
if __name__ == '__main__':
result = 0
for prime in primes(1000000):
result += all(is_prime(int("".join(rot))) for rot in rotations(list(str(prime))))
print(result)
#!/usr/bin/env python from math_tools import is_prime """https://projecteuler.net/problem=58""" if __name__ == '__main__': side = 1 corner = 1 primes = 0 while True: side += 2 for i in range(4): corner += side - 1 if is_prime(corner): primes += 1 if (float(primes) / ((side - 1) * 2 + 1)) < 0.1: print(side) break
# -*- coding: utf-8 -*-
"""
Created on 2014-09-23
Last edited on 2014-09-23
@author: Ew3n
"""
import math_tools
range_min = 10000
range_max = 10050
my_list = []
for i in range(range_min, range_max+1):
if math_tools.is_prime(i):
my_list.append(i)
print(*my_list, sep=", ")
#!/usr/bin/env python
from math_tools import is_prime
"""https://projecteuler.net/problem=58"""
if __name__ == "__main__":
side = 1
corner = 1
primes = 0
while True:
side += 2
for i in range(4):
corner += side - 1
if is_prime(corner):
primes += 1
if (float(primes) / ((side - 1) * 2 + 1)) < 0.1:
print(side)
break
#!/usr/bin/env python
from math_tools import rotations, primes, is_prime
"""https://projecteuler.net/problem=35"""
if __name__ == '__main__':
result = 0
for prime in primes(1000000):
result += all(
is_prime(int("".join(rot))) for rot in rotations(list(str(prime))))
print(result)
#!/usr/bin/env python from math_tools import primes, is_prime """https://projecteuler.net/problem=49""" if __name__ == '__main__': for prime in primes(): prime2 = prime + 3330 prime3 = prime2 + 3330 if ( prime != 1487 and len(str(prime)) == 4 and sorted(str(prime)) == sorted(str(prime2)) == sorted(str(prime3)) and is_prime(prime2) and is_prime(prime3) ): print str(prime) + str(prime + 3330) + str(prime + 6660) exit()
#!/usr/bin/env python from math_tools import is_prime, primes """https://projecteuler.net/problem=27""" if __name__ == '__main__': generator_product = None max_primes_generated = None for b in primes(1000): for a in range(-999, 1000, 2): n = 0 primes_generated = 0 while True: if not is_prime((n ** 2) + (a * n) + b): break primes_generated += 1 n += 1 if primes_generated > max_primes_generated: max_primes_generated = primes_generated generator_product = a * b print(generator_product)
We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
What is the largest n-digit pandigital prime that exists?
"""
# Pandigital numbers with 1,2,5,8,9 digits cannot be prime because for the case of 2,5,8,9 - the digits will sum up to a multiple of 3 making the result divisible by 3.
# Also such numbers can not end in 2,4,5,6,8 or it will be composite.
# This leaves only us with pandigital numbers with 3,4,6,7 digits to check.
from itertools import permutations
from math_tools import is_prime
pandigital = set()
pandigital.update(permutations([x for x in range(1,1+3)]))
pandigital.update(permutations([x for x in range(1,1+4)]))
pandigital.update(permutations([x for x in range(1,1+6)]))
pandigital.update(permutations([x for x in range(1,1+7)]))
def is_composite(t):
if t[-1] == 2: return True
if t[-1] == 4: return True
if t[-1] == 5: return True
if t[-1] == 6: return True
if t[-1] == 8: return True
return False
not_composite = filter(lambda x : not is_composite(x), pandigital)
nums = map(lambda t : int(''.join(map(str,t))), not_composite)
primes = filter(lambda x : is_prime(x), nums)
print max(primes)
#!/usr/bin/env python
from math_tools import primes, is_prime
"""https://projecteuler.net/problem=49"""
if __name__ == "__main__":
for prime in primes():
prime2 = prime + 3330
prime3 = prime2 + 3330
if (
prime != 1487
and len(str(prime)) == 4
and sorted(str(prime)) == sorted(str(prime2)) == sorted(str(prime3))
and is_prime(prime2)
and is_prime(prime3)
):
print str(prime) + str(prime + 3330) + str(prime + 6660)
exit()
#!/usr/bin/env python from math_tools import is_prime """https://projecteuler.net/problem=3""" if __name__ == '__main__': cmp = 600851475143 print(next(div for div in xrange(int(cmp ** 0.5), 1, -1) if cmp % div == 0 and is_prime(div)))
"""
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below two million.
"""
from math_tools import is_prime
primes = [2]
for x in range(3, int(2e6), 2):
if is_prime(x) == True:
primes.append(x)
ans = sum(primes)
print ans
# -*- coding: utf-8 -*-
"""
Created on 2014-09-23
Last edited on 2014-09-23
@author: Ew3n
"""
import math_tools
n = 100000000
while not(math_tools.is_prime(n)):
n += 1
print(n)
