def problem(limit):
pr_gen = primes_gen()
sum_primes = 0
primes = []
while sum_primes < limit:
prime = next(pr_gen)
sum_primes += prime
primes.append(prime)
length = len(primes)
while True:
num = sum(primes[:length])
start = 0
while num < limit:
if miller_rabin_test(num):
if length >= 3:
print('{} = {} + {} + ... + {}'.format(
num, primes[start], primes[start + 1],
primes[start + length - 1]))
else:
print('{} = {}'.format(
num, ' + '.join(map(str,
primes[start:start + length]))))
print(
'The longest sum of consecutive primes below {} that adds to a prime, '
'contains {} terms, and is equal to {}.'.format(
limit, length, num))
return num
else:
if (start + length) >= len(primes):
primes.append(next(pr_gen))
num += primes[start + length] - primes[start]
start += 1
length -= 1
def problem():
max_num_primes, possible_a, possible_b = 0, 0, 0
for b in range(2, 1001):
if miller_rabin_test(b):
endpoint = floor(b ** 0.5)
for a in range(-2 * endpoint, 2 * endpoint + 1, 1):
num_primes = 0
for n in range(0, b):
if miller_rabin_test(quadratic(n, a, b)):
num_primes += 1
else:
break
if num_primes > max_num_primes:
possible_a = a
possible_b = b
max_num_primes = num_primes
return possible_a, possible_b, max_num_primes
def check(xs):
probables = []
for x in xs:
for i in range(1, 10):
new_x = int(str(i) + str(x))
if miller_rabin_test(new_x):
probables.append(new_x)
pow_10 = 10
while pow_10 < new_x:
if miller_rabin_test(new_x // pow_10):
pow_10 *= 10
else:
break
else:
truncatable.append(new_x)
if len(truncatable) < 11:
check(probables)
def problem():
max_prime = 0
flag = False
# 1 + 2 + ... + 9 = 45, 45 % 3 => 9-digit pandigital is not prime.
for pw in range(8, 0, -1):
for permut in permutations(range(1, pw + 1)):
num = 0
for i in permut:
num *= 10
num += i
if miller_rabin_test(num):
max_prime = max(max_prime, num)
flag = True
if flag:
break
return max_prime
def problem(lim):
circular_primes = list(filter(lambda x: x < lim, [2, 3, 5]))
for num in range(7, lim, 2):
temp = num
digits = []
while temp > 0:
digits.append(temp % 10)
temp //= 10
if not ({0, 2, 4, 6, 8, 5} & set(digits)):
for _ in range(len(digits)):
rotation = 0
for i in digits:
rotation *= 10
rotation += i
if miller_rabin_test(rotation):
digits = digits[1:] + digits[:1]
else:
break
else:
circular_primes.append(num)
return circular_primes