def special_sum(up_to_n):
polling_interval = 1000000
prime_list = [p for p in primes(int((up_to_n + 1) ** 0.5) + 1)]
tot = 0
t0 = time.time()
for j in xrange(2, up_to_n, 4):
if is_special(j, prime_list):
print(j)
tot += j
if (j - 2) % polling_interval == 0:
t = time.time() - t0
t0 = time.time()
print("[{:.2f}s, {:,.0f}/s] {:,d} out of {:,d}".format(t, polling_interval / t, j - 2, up_to_n))
return tot
def gen_special(up_to_n):
yield 2
print("generating list...")
prime_list = primes(up_to_n / 2)
print("have primes. finding max number of factors.")
max_length = next(j for j, _ in enumerate(prime_list) if prod(prime_list[:j]) > up_to_n)
print("max factors is {:d}. Analyzing factors.".format(max_length))
for j in range(1, max_length + 1):
print("Analyzing factors of length {:d}".format(j))
for factors in combinations(prime_list[1:], j):
print(factors)
n = 2 * prod(factors)
if n > up_to_n:
break
if all(is_prime(divisor + n / divisor, prime_list) for divisor in divisor_gen_from_factors(list(factors) + [2])):
yield n
def divides_small_repunit(primes_to=100):
prime_list = primes(primes_to)
found_set = set()
same_count = 0
prime_gen = prime_generator()
while same_count < 5: # wait for list to stabilize
found_set_len = len(found_set)
j = prime_gen.next()
for p in prime_list:
if repunit_factor(j, p):
found_set.add(p)
if found_set_len == len(found_set):
same_count += 1
else:
same_count = 0
return sum(prime_list) - sum(found_set)
def scratch(up_to_n):
prime_list = [p for p in primes(int((up_to_n + 1) ** 0.5) + 1)]
t0 = time.time()
for j in xrange(2, up_to_n, 4):
if is_special(j, prime_list):
print(j, list(factor_num(j)))
def solve(upper_bound):
tot = 0
prime_list = primes(int(1.01 * upper_bound))
for idx, prime in (j for j in enumerate(prime_list) if 5 <= j[1] <= upper_bound):
tot += connection(*prime_list[idx:idx + 2])
print tot
# 10001st prime
from utilities.primes import primes
print "10001st prime number is: {}".format(primes(1000000)[10000])
def get_largest_pan_digital_prime():
prime_nums = primes(10000000)
return max([x for x in prime_nums if is_pan_digital(x)])
def test_primes():
assert_list_equal(primes(20), list(small_primes))
