def solve():
limit = 50000000
primes_a = list(gen_primes(int(limit**0.5)))
primes_b = list(gen_primes(int(limit**0.34)))
primes_c = list(gen_primes(int(limit**0.25)))
result = set()
for a in primes_a:
for b in primes_b:
for c in primes_c:
result.add(a**2 + b**3 + c**4)
print len([x for x in result if x < limit])
def solve():
total = 0
for prime in gen_primes():
if prime > 2000000:
break
total += prime
return total
def solve():
result = []
primes = set()
for x in gen_primes():
primes.add(x)
if x <= 7:
continue
if all(y in primes for y in truncate_left(x)) and all(y in primes for y in truncate_right(x)):
result.append(x)
if len(result) == 11:
break
return sum(result)
def solve():
x = 5
while True:
if not is_prime(x):
for p in gen_primes(x):
a = x - p
if a % 2 == 0:
b = a / 2
b = sqrt(b)
if b.is_integer():
break
else:
return x
x += 2
def solve():
primes = list(gen_primes(1000000))
primes_ = set(primes)
result = defaultdict(list)
for i in xrange(len(primes)):
s = 0
l = 0
for j in xrange(i, len(primes)):
s += primes[j]
l += 1
if s in primes_:
result[l].append(s)
if s > 1000000:
break
return max(result.iteritems(), key=operator.itemgetter(0))[1][0]
def solve():
d = 1
primes = []
phi = None
while True:
for p in gen_primes():
d *= p
primes.append(p)
phi = totient(d)
if phi / float(d-1) < LIMIT:
if p > 2:
primes.pop()
d /= p
phi = totient(d)
break
else:
return d
def solve():
count = 1
for prime in gen_primes():
if count == 10001:
return prime
count += 1
def solve():
total = 0
for p in gen_primes(40000000):
if chain_length(p) == 25:
total += p
return total
def solve():
primes = set(gen_primes(1000000))
return len([x for x in primes if all(y in primes for y in rotations(x))])
def solve():
for p in gen_primes():
if check_prime(p):
return p
from common import gen_primes
DIGITS = map(str, range(10))
PRIMES = set(gen_primes(1000000))
def check_prime(p):
p = str(p)
for d in set(p):
replacements = [int(p.replace(d, new_d)) for new_d in DIGITS]
replacements = filter(lambda x: len(str(x)) == len(p), replacements)
replacements = filter(lambda x: x in PRIMES, replacements)
if len(replacements) >= 8:
return True
def solve():
for p in gen_primes():
if check_prime(p):
return p
def main():
print 'Solution:', solve()
if __name__ == '__main__':
main()