def ID050():
limit = 1000000
primes = EulerFuncs.primes_below(limit)
check_prime = set(primes)
p_sums = [0]
s = 0
# Sum of consecutive primes
for p in primes:
s += p
if s >= limit: break
p_sums.append(s)
longest = 0
prime = 0
# Checks sum of all combinations of primes that sums < limit
for n, p_sum_small in enumerate(p_sums):
for j, p_sum_big in enumerate(p_sums):
num_btw = j-n
difference = p_sum_big - p_sum_small
# 'in' for a set is much faster than with a list
if num_btw > longest and difference in check_prime:
longest = num_btw
prime = difference
return "num consecutive: %s, prime: %s" % (longest, prime)
def _iterate_totient(limit):
"""Iteratively calculates the totient function
for values under a limit
"""
primes = EulerFuncs.primes_below(limit)
sieve = [n for n in xrange(limit)]
for p in primes:
mult = p
while mult < limit:
sieve[mult] *= (1-1/float(p))
mult += p
return sieve
def ID038():
n = 9182
stop = 10000
limit = 1000000000
largest = 918273645
for n in xrange(n, stop):
product_concat = str(n)
n = 2
while 1:
product = n * n
n += 1
if int(product_concat + str(product)) > limit:
break
product_concat += str(product)
if int(product_concat) > largest and EulerFuncs.is_pandigital(product_concat):
largest = int(product_concat)
return largest
def test_pandigital():
print EulerFuncs.is_pandigital(12345678)
print EulerFuncs.is_pandigital(123456789)
print EulerFuncs.is_pandigital(1234567890)
print EulerFuncs.is_pandigital(203456789)
print EulerFuncs.is_pandigital(234567189)
'''
Created on Jan 8, 2012
@author: Admin
'''
import EulerFuncs
import timeit
def test_sieve_time():
TRIALS = 20
t = timeit.Timer("EulerFuncs.primes_below(1000000)", "import EulerFuncs")
print "Own: %.4f s/pass" % (t.timeit(number=TRIALS)/TRIALS)
t = timeit.Timer("EulerFuncs.primes_under(1000000)", "import EulerFuncs")
print "Old: %.4f s/pass" % (t.timeit(number=TRIALS)/TRIALS)
def test_pandigital():
print EulerFuncs.is_pandigital(12345678)
print EulerFuncs.is_pandigital(123456789)
print EulerFuncs.is_pandigital(1234567890)
print EulerFuncs.is_pandigital(203456789)
print EulerFuncs.is_pandigital(234567189)
if __name__ == "__main__":
print sum(EulerFuncs.primes_below(1000)[3:24])
print EulerFuncs.primes_below(1000)[23]
#!/usr/bin/env python
# date: Apr 23, 2012
import EulerFuncs
import itertools
def str_permute(s):
perms = list(itertools.permutations(s))
for i in xrange(len(perms)):
perms[i] = "".join(str(i) for i in perms[i])
return perms
# find primes 1000 <= primes < 10000
limit = 10000
primes = EulerFuncs.primes_below(limit)
primes = primes[primes.index(1009):]
primes_set = set(primes)
for i in xrange(len(primes)):
for j in xrange(i+1, len(primes)):
prime1 = primes[i]
prime2 = primes[j]
diff = prime2 - prime1
prime3 = prime2 + diff
# check if prime3 is prime
if prime3 in primes_set:
prime1_perm = str_permute(str(prime1))
# check if the three numbers are permutations of one another
if str(prime2) in prime1_perm and str(prime3) in prime1_perm:
print prime1, prime2, prime3
