def maxconsecutiveprime(x):
ps = primes(x)
s = 0
for i, p in enumerate(ps):
s += p
if s > x:
break
ps2 = ps[:i]
l = len(ps2)
for i in range(l)[::-1]:
for j in range(l - i)[::-1]:
pp = ps2[j:j + i + 1]
if sum(pp) in ps:
return sum(pp), len(pp), pp
#! /usr/bin/env python3
'''
Problem 46 - Project Euler
http://projecteuler.net/index.php?section=problems&id=046
'''
import math
from mathtools import primes
if __name__ == '__main__':
N = 1_000_0
ps = primes(N)
odd_composite_num = list(set(range(5, N+1, 2)) - set(ps))
for i in odd_composite_num:
for sq in range(1, int(math.sqrt(i/2))+1)[::-1]:
if (i - 2 * (sq ** 2)) in ps:
break
else:
print(i)
break
def main(args):
return mt.item_by_index(mt.primes(), args.prime_index)
#! /usr/bin/env python3
'''
Problem 26 - Project Euler
http://projecteuler.net/index.php?section=problems&id=026
'''
from mathtools import primes
def countcycle(x):
count, n = 0, 1
while n % x == n:
count += 1
n = n * 10
while n % x != 1:
if n % x == 0:
return 0
count += 1
n = (n % x) * 10
return count
if __name__ == '__main__':
n = 1000
ps = primes(n)
ps.remove(2)
ps.remove(5)
cclist = map(lambda x: (x, countcycle(x)), ps)
print(max(cclist, key=(lambda x: x[1])))
#! /usr/bin/env python3
'''
Problem 7 - Project Euler
http://projecteuler.net/index.php?section=problems&id=7
'''
from mathtools import primes
NUM = 10_001
if __name__ == '__main__':
pmax = 110000
ps = primes(pmax)
while len(ps) < NUM:
pmax += 10000
ps = primes(pmax)
else:
print(str(ps[NUM - 1]) + ' is the {}st prime number.'.format(NUM))
def main(args):
return mt.item_by_index(mt.primes(), args.prime_index)
#! /usr/bin/env python3
'''
Problem 49 - Project Euler
http://projecteuler.net/index.php?section=problems&id=049
'''
from mathtools import primes
from itertools import combinations
from functools import reduce
from operator import add
def samedigits(*xs):
if len(xs) < 2:
return True
x = set(str(xs[0]))
return all([set(str(y)) == x for y in xs[1:]])
if __name__ == '__main__':
ps = list(filter(lambda x: x > 999, primes(9999)))
cs = [c for c in combinations(ps,2) if samedigits(*c) and (2 * max(c) - min(c)) in ps]
ans = []
for c in cs:
x, y = min(c), max(c)
z = 2 * y - x
if samedigits(x, y, z):
ans.append((x, y, z))
print(ans)
print(list(map(lambda x: reduce(add, map(str, x)), ans)))