def test_primes():
primes_list = itertools.takewhile(lambda x: x <= 100, math_ext.primes())
primes_list = list(primes_list)
assert primes_list == [
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,
71, 73, 79, 83, 89, 97
]
def test_has_number_of_replaced_primes():
assert problem.has_number_of_replaced_primes(121313, 8)
primes = math_ext.primes()
p = next(primes)
while p < 56003:
assert not problem.has_number_of_replaced_primes(p, 7)
p = next(primes)
assert problem.has_number_of_replaced_primes(56003, 7)
def solve():
prime_pair_sets = []
for new_p in math_ext.primes():
for prime_pair_set in prime_pair_sets:
if is_prime_pair_set(new_p, prime_pair_set):
new_prime_pair_set = (new_p, ) + prime_pair_set
if len(new_prime_pair_set) == 5:
return sum(new_prime_pair_set)
prime_pair_sets.append(new_prime_pair_set)
prime_pair_sets.append((new_p, ))
def prime_decompose(x):
if x == 1:
return [1]
factors = []
for p in math_ext.primes():
if p > x:
break
while x % p == 0:
factors.append(p)
x /= p
return factors
def get_max_consecutive_prime_sum(threashold):
primes = list(slice_seq(math_ext.primes(), 0, threashold))
start, end = 0, 1
for i in range(len(primes)):
for j in range(i + end - start, len(primes)):
p = sum(primes[i:j])
if p >= threashold:
break
if math_ext.is_prime(p):
start, end = i, j
return sum(primes[start:end])
def solve():
primes = itertools.takewhile(lambda x: x < 1000000, math_ext.primes())
circular_primes = []
for p in primes:
circular_numbers = get_circular_numbers(p)
if any([n % 2 == 0 for n in circular_numbers]):
continue
if min(circular_numbers) < p:
continue
if is_circular_prime(p):
circular_primes += get_circular_numbers(p)
return len(circular_primes)
def solve():
return sum(itertools.takewhile(lambda x: x <= 2000000, primes()))
def get_4_digit_primes():
primes = math_ext.primes()
primes = itertools.dropwhile(lambda n: n < 1000, primes)
primes = itertools.takewhile(lambda n: n < 10000, primes)
return primes
def solve():
for p in math_ext.primes():
if has_number_of_replaced_primes(p, 8):
return p
def get_truncable_primes():
return filter(is_truncatable_prime, math_ext.primes())
def solve():
index = 10001
index_th_prime_iter = itertools.islice(primes(), index - 1, index)
index_th_prime = list(index_th_prime_iter)[0]
return index_th_prime
