def split_on_primes(before: tuple, n: int, after: tuple):
if n < 10: return
idx = 0
left = 0
lst = list(map(int, list(str(n))))
while idx < len(lst):
left *= 10
left += lst[idx]
right = join(lst[idx + 1:])
if is_prime(left):
tup = []
if left > 0:
tup.append(left)
if right > 0:
tup.append(right)
splits.add(before + tuple(tup) + after)
if left and right:
if left > 0:
split_on_primes(before, left, (right, ) + after)
if right > 0:
split_on_primes(before + (left, ), right, after)
idx += 1
res = []
for s in splits:
if is_prime(s[-1]):
res.append(s)
return res
def primes(limit):
'''Generates prime numbers up to limit. Pass 'None' as argument to infinite loop'''
if not limit: print('WARNING: Running in infinite loop mode')
yield 2
i = 3
while not limit or i < limit:
if is_prime(i):
yield i
i += 2
def possible_primes(num_digits: int):
primes = set()
digits = [n for n in range(1, 10)]
for c in combinations(digits, num_digits):
if num_digits == 8 and 2 in c and 3 in c and 5 in c and 7 in c:
continue
for p in permutations(c):
number = join(p)
if is_prime(number):
primes.add(number)
return primes
def possibilities(n, d):
repeat = True
for i in range(10):
if not repeat: break
t = [True] * (n-i) + [False] * i
print('__________')
for p in set(permutations(t)):
for x in fill(p, d):
if is_prime(x) and x > 10**(n-1):
repeat = False
print(x)
yield(x)
def run(n):
odds = 0
even_primes = set()
for i in range(2, n):
if is_prime(i):
period = frac_decompose(i)
if period % 2:
odds += 1
else:
even_primes.add(i)
else:
if is_possibly_odd_period(i, even_primes):
x = frac_decompose(i)
if x % 2:
odds += 1
return odds
def primetest(n):
if n not in prime_cache:
prime_cache[n] = is_prime(n)
return prime_cache[n]
def circular_prime(n):
for p in rotate(n):
if not is_prime(p):
return False
return True
def prime_diffs(n):
neighbors = get_neighbors(n)
count = 0
for neighbor in neighbors:
if is_prime(abs(n - neighbor)): count += 1
return count
def primetest(n):
if n in primes:
return primes[n]
else:
primes[n] = is_prime(n)
return primes[n]