class Problem58:
def __init__(self):
self.primeChecker = PrimeChecker()
self.primeChecker.init_prime_factoring()
@staticmethod
def get_diagonals_from_spiral_of_size(size, diagonals=None):
counter = 1
if diagonals is None:
diagonals = []
for i in range(0, int((size-1)/2)):
for _ in range(0, 4):
counter += 2 + 2*i
diagonals.append(counter)
else:
i = int((size-1)/2) - 1
counter = int(diagonals[-1])
for _ in range(0, 4):
counter += 2 + 2*i
diagonals.append(counter)
return diagonals
def answer(self):
size = 1
ratio = 100
diagonals = None
total_primes = 0
while ratio >= 0.10:
size += 2
diagonals = self.get_diagonals_from_spiral_of_size(size, diagonals)
total = (size-1)/2 * 4 + 1
total_primes += len([x for x in diagonals[-4:-1] if self.primeChecker.is_prime(x)])
ratio = total_primes / total
return size
def tri_sequence_is_prime_and_permutation(self, start, step):
for n in range(0, 3):
if not PrimeChecker.is_prime(start + n * step):
return False
for n in range(0, 3):
if not self.is_permutation_of(start + n * step, start):
return False
return True
def get_longest_sum_of_consecutive_primes_below(n):
longest_sequence_length = 0
longest_sum = 0
primes = PrimeChecker.primes_below(n)
for i in range(0, len(primes)):
for j in range(i + 1, len(primes) - 1):
prime_sum = sum(primes[i:j])
if prime_sum >= n:
break
if PrimeChecker.is_prime(prime_sum) and j - i > longest_sequence_length:
longest_sequence_length = j - i
longest_sum = prime_sum
return longest_sequence_length, longest_sum
class Problem60:
def __init__(self, prime_limit):
self.primeChecker = PrimeChecker()
self.primeChecker.init_prime_factoring()
self.primes = PrimeChecker.primes_below(prime_limit)
self.primes.remove(2)
self.pairs = self.build_pairs(self.primes)
def build_pairs(self, primes):
pairs = dict()
for p1 in primes:
if p1 == 5:
continue
pairs[p1] = set()
for q in range(primes.index(p1), len(primes)):
p2 = primes[q]
if self.primeChecker.is_prime(int(str(p1) + str(p2))) and \
self.primeChecker.is_prime(int(str(p2) + str(p1))):
pairs[p1].add(p2)
return pairs
def answer(self):
lowest = 10000000
for p1 in self.pairs:
for p2 in self.pairs[p1]:
set_a = self.pairs[p1] & self.pairs[p2]
if len(set_a) > 0:
for p3 in set_a:
set_b = set_a & self.pairs[p3]
if len(set_b) > 0:
for p4 in set_b:
set_c = set_b & self.pairs[p4]
if len(set_c) > 0:
total = sum([p1, p2, p3, p4] + list(set_c))
if total < lowest:
lowest = total
return lowest
def test_27ShouldNotBeAPrime(self):
self.assertFalse(PrimeChecker.is_prime(27))
def test_47ShouldBeAPrime(self):
self.assertTrue(PrimeChecker.is_prime(47))
