from lib.eratosthenes import sieve target = 2000000 print(sum(sieve(target)))
bound = 1000
from lib.eratosthenes import sieve
primes = set(sieve(100000))
is_prime = lambda x: x in primes
def quadratic(n, a, b):
return n * n + a * n + b
def test_quadratic(a, b):
n = 0
while True:
if is_prime(abs(quadratic(n, a, b))): n += 1
else: break
return n
primes = set(filter(is_prime, range(0, bound)))
max_primes = 0
max_primes_mul = 0
for i in primes:
for j in primes:
counter = max(test_quadratic(i, j), test_quadratic(-i, -j),
test_quadratic(-i, j), test_quadratic(i, -j))
if counter > max_primes:
max_primes = counter
max_primes_mul = i * j
print(
max_primes_mul
) # NOTE, test this with a - sign since one of i or j might be negative, and makes the code easier
from lib.eratosthenes import sieve
primes_list = sieve(999999)[5781:]
primes = set(primes_list)
is_prime = lambda x: x in primes
def replace(string, replacement, *pos):
new, i = '', 0
for p in pos:
new += string[i:p] + replacement
i = p + 1
return new + string[i:]
def generate_family(n, digit):
return [
replace(n, str(x), *[x for x in range(len(n)) if n[x] == digit])
for x in (range(10) if n[0] != digit else range(1, 10))
]
def is_8family(family):
return sum(1 for x in family if is_prime(int(x))) == 8
def search():
for dig in '012':
for number in (d for d in primes_list if dig in str(d)[:-1]):
if is_8family(generate_family(str(number), dig)):
return number
from lib.eratosthenes import sieve
primes = set(sieve(20000000))
def is_prime(n):
return n in primes
def verify_left(n):
if len(n) == 1:
return True
if not is_prime(int(n)):
return False
if verify_left(n[1:]):
return True
return False
def verify_right(n):
if len(n) == 1:
return True
if is_prime(int(n)):
return False
if verify_right(n[:-1]):
return True
return False
def verify(n):
if not is_prime(n): return False
ns = str(n)