def candidate_triplets():
""" just solving the special case of 3330-separated primes
"""
sieve = prime.get_primes_up_to(10000)
for i in range(1000, 10000):
if i in sieve and i + 3330 in sieve and i + 6660 in sieve:
yield (i, i+3330, i+6660)
def get_least_violation():
global primes
primes = prime.get_primes_up_to(int(1e6))
for i in itertools.count(start=1, step=2):
if is_composite(i):
for residual in get_residuals(i):
if residual / 2 == residual // 2:
sq = math.sqrt(residual // 2)
if math.floor(sq) == sq:
break
else:
return i
def get_next_quad():
prev_max = 0
current_max = int(1e6)
while True:
primes = prime.get_primes_up_to(current_max)
composites = [i for i in range(prev_max, current_max) if i not in primes]
for i, comp in enumerate(composites):
if composites[i+3] - comp == 3:
yield comp
prev_max = current_max
current_max *= 10
def make_n2_sum(n):
sum_lengths = Counter()
prime_set = prime.get_primes_up_to(n)
sorted_primes = sorted(prime_set)
sums = [0]
current_sum = 0
for p in sorted_primes:
current_sum += p
sums.append(current_sum)
max_length = 0
for p in sorted_primes:
for length, prime_sum in enumerate(sums):
if max_length < length and prime_sum in prime_set:
max_length = length
sum_lengths[prime_sum] = max(sum_lengths[prime_sum], length)
sums = [i - p for i in sums[1:]]
if len(sums) < max_length:
break
return sum_lengths
#!/usr/bin/env python3
import prime
def generate_rotations(n):
digits = [d for d in str(n)]
rotations = set()
for i in range(len(digits) - 1):
digits = [digits[-1]] + digits[:-1]
rotations.add(int(''.join(digits)))
return rotations
if __name__ == '__main__':
circular = []
primes = prime.get_primes_up_to(int(1e6))
while primes:
p = primes.pop()
rotations = generate_rotations(p)
# special case for 11
if len(rotations) > 0 and next(iter(rotations)) == p:
circular.append(p)
elif primes & rotations == rotations:
print(p, rotations)
circular.append(p)
circular += rotations
primes -= rotations
print(circular)
print(len(circular))
def test_sieve_some_primes(self):
sieve = prime.get_primes_up_to(max(self.sample_primes))
self.assertFalse(self.sample_primes - sieve)
