def pandigitals():
primes = list(generate_primes(17))
return (
int(''.join(pandigital)) for pandigital in permutations('0123456789')
# d2d3d4 is divisible by 2 iff d4 is divisible by 2
if int(pandigital[3]) % 2 == 0
# d4d5d6 is divisible by 5 iff d6 is divisible by 5 (= 0 or 5)
# d6d7d8 is divisible by 11 -> d6 can't be 0 (011, 022, ...)
if int(pandigital[5]) == 5 if are_digits_divisible(pandigital, primes))
def consecutive_primes():
primes_list = list(generate_primes(1000000))
primes_set = set(primes_list)
for i in range(10):
prime_sum = 0
for j in range(i, len(primes_list)):
prime_sum += primes_list[j]
if prime_sum in primes_set:
yield j - i + 1, prime_sum
def solve():
result = 1
primes = list(generate_primes(20))
i = 0
while result * primes[i] < 1000000:
result *= primes[i]
i += 1
return result
def pandigitals():
primes = list(generate_primes(17))
return (int(''.join(pandigital))
for pandigital in permutations('0123456789')
# d2d3d4 is divisible by 2 iff d4 is divisible by 2
if int(pandigital[3]) % 2 == 0
# d4d5d6 is divisible by 5 iff d6 is divisible by 5 (= 0 or 5)
# d6d7d8 is divisible by 11 -> d6 can't be 0 (011, 022, ...)
if int(pandigital[5]) == 5
if are_digits_divisible(pandigital, primes))
def solve():
limit = 10000
primes = set(generate_primes(limit))
return next(int(''.join(map(str, [a, b, c(a, b)])))
for a in primes.intersection(range(1001, limit, 2))
for b in primes.intersection(range(a + 2, limit, 2))
if a != 1487
if c(a, b) in primes
if sorted(str(a)) == sorted(str(b)) == sorted(str(c(a, b))))
def solve():
primes = list(generate_primes(30))
i = 0
n = 1
limit = 15499 / 94744
while resilience(n * primes[i]) >= limit:
n *= primes[i]
i += 1
for c in (n for n in range(2, primes[i - 1]) if n not in primes):
if resilience(n * c) < limit:
return n * c
def solve():
primes = math_helper.generate_primes(7500000)
heap = []
for value in primes:
heappush(heap, value)
n = 1
for power in range(500500):
head = heappop(heap)
n *= head
n %= 500500507
heappush(heap, head ** 2)
return n
def truncatables():
primes = set(generate_primes(1000000))
return (n for n in primes if n > 10 if is_truncatable(n, primes))
def truncatables():
primes = set(generate_primes(1000000))
return (n for n in primes
if n > 10
if is_truncatable(n, primes))
def solve():
primes = set(generate_primes(100000))
r = range(-999, 1000, 2)
_, a, b = max((count_primes(a, b, primes), a, b) for a in r for b in r)
return a * b
def solve():
primes = set(generate_primes(1000000))
return len(list(generate_circulars(primes)))
def solve():
primes = set(generate_primes(1000))
return next(n for n in count() if has_four_factors(primes, n))
def solve():
return sum(generate_primes(2000000))
def solve():
return list(generate_primes(200000))[10000]
