from EulerUtils import genPrimes limit = 50000000 lim1 = limit ** 0.33 lim2 = limit ** 0.25 primes = genPrimes(int(limit ** 0.5)) cubes = [i ** 3 for i in primes if i < lim1] fourths = [i ** 4 for i in primes if i < lim2] P = set() for a in primes: a = a ** 2 for b in cubes: b += a if b > limit: break for c in fourths: c += b if c >= limit: break P.add(c) print len(P)
from time import clock
from math import ceil
from math import log10
from EulerUtils import genPrimes
primes = genPrimes(100)
def up(n):
return int(ceil(n))
l = len(primes)
def sol(i, pLim):
s = 0
if i == len(primes):
return 1
else:
p = primes[i]
r = log10(p)
lim = up((9 - pLim) / r)
for x in range(lim):
s += sol(i + 1, pLim + x * r)
return s
t = clock()
print sol(0, 0) + 1
print clock() - t
from time import clock
from EulerUtils import genPrimes
t = clock()
primes = set(genPrimes(10000))
for prime in primes:
if 1000 < prime < 3340:
a = prime + 3330
b = prime + 6660
if a in primes and b in primes:
if set(str(prime)) == set(str(a)) == set(str(b)):
print str(prime) + str(a) + str(b), clock() - t
from time import clock
from EulerUtils import genPrimes
t = clock()
primes = genPrimes(1000)[3:]
pows = [10 ** i for i in range(1, 1000)]
m, n = 0, 0
for d in primes:
p = [i for i in pows if (i - 1) % d == 0][0]
if p > m:
m, n = p, d
print clock() - t, n
from EulerUtils import genPrimes
lim = 1000000
sum = 0
sums = []
primes = genPrimes(lim)
for prime in primes:
sum += prime
if sum < lim:
sums.append(sum)
else:
break
m, n = 0, 0
l = len(sums)
primes = set(primes)
for i in range(l):
for j in range(i + m, l):
x = sums[j] - sums[i]
if j - i > m and x in primes:
n = x
m = j - i
print m, n