def answer():
primes = sieve(32)
d, x = 1, 1
for prime in primes:
d *= prime
x *= prime - 1
for n in range(2, prime):
if x*n/(d*n - 1) < 15499/94744:
return d*n
def answer():
found = 2
primes = sieve(100)
while found:
perms = [1] + [0] * found
for a in range(len(primes)):
for b in range(primes[a], found + 1):
perms[b] += perms[b - primes[a]]
if perms[found] > 5000:
return found
found += 1
def answer():
count = set()
primes = sieve(7071)
for a in primes:
for b in primes:
d = a**4 + b**3
if d >= 50000000:
break
for c in primes:
e = c*c + d
if e >= 50000000:
break
count.add(e)
return len(count)
from euler_helpers import sieve
primes_up_to_20 = sieve(20)
prod_factors = [0]*21 # each element represents number of that index as a factor
for i in range(1,21):
i_factors = [0]*21
d = i
while d not in primes_up_to_20:
for prime in primes_up_to_20[1:]:
if d%prime==0:
i_factors[prime] += 1
d /= prime
break
i_factors[d] += 1
prod_factors = [ max([prod_factors[j],i_factors[j]]) for j in range(len(i_factors))]
print prod_factors
prod = reduce(lambda x,y:x*y, [i**prod_factors[i] for i in range(len(prod_factors)) ],1)
print 'Smallest product easily divisble by numbers 1-20 is %d' % (prod,)
from euler_helpers import sieve print sieve(150000)[10000]