def trunk_prime(n):
if n == 2 or n == 3 or n == 5 or n == 7:
return False
if not is_prime(n):
return False
digs = [i for i in str(n)]
for i in range(1, len(digs)):
right = int("".join(digs[i:]))
# print(right)
left = int("".join(digs[:i]))
if not is_prime(right) or not is_prime(left):
return False
return True
def sequece_length(a, b):
n = 0
while True:
numb = abs(quad(n, a, b))
if not is_prime(numb):
return n
n += 1
def _strong_harshad_numbers(n, digits_sum):
for i in range(10):
next_n = (10 * n) + i
dig_sum_i = digits_sum + i
if next_n <= LIMIT and next_n % (dig_sum_i) == 0:
if is_prime((next_n / dig_sum_i)):
rthp.update(_harshad_primes(next_n))
_strong_harshad_numbers(next_n, dig_sum_i)
def prime_sums(n):
# this is the same as my coin sums code
primes = [p for p in range(2, n) if is_prime(p)]
ok_primes = [i for i in primes if i < (n + 1)]
# print(ok_coins)
sums = [0] * (n + 1)
sums[0] = 1
for prime in ok_primes:
for i in range(prime, n + 1):
sums[i] += sums[abs(i - prime)]
return sums[n]
def p046():
n = 3
prime_numbers = set()
prime_numbers.add(2)
while True:
if is_prime(n):
prime_numbers.add(n)
else:
for p in prime_numbers:
if sqrt(((n - p) / 2)) == int(sqrt(((n - p) / 2))):
break # break if it works with the conjecture
else:
return n
n += 2
def spiral_prime_iterator(ratio_bound):
ratio = 0.5
i = 0
addon = 2
adds = 0
no_primes = 0
total_nums = 0
while ratio > ratio_bound:
if adds > 0 and adds % 4 == 0:
addon += 2
i += addon
adds += 1
total_nums += 1
if is_prime(i + 1):
no_primes += 1
ratio = truediv(no_primes, total_nums)
return addon + 1
def p049():
four_dig_primes = [i for i in range(1000, 10000) if is_prime(i)]
num_4dig_primes = len(four_dig_primes)
prime_perms = defaultdict(list)
for prime in four_dig_primes:
sorted_digs = tuple(sorted(digits_list(prime)))
prime_perms[sorted_digs].append(prime)
topop = [k for k, v in prime_perms.items() if len(v) < 3]
for toop in topop:
prime_perms.pop(toop)
validsets = []
for k, v in prime_perms.items():
for combo in combinations(v, 3):
if combo[1] - combo[0] == combo[2] - combo[1]:
validsets.append(combo)
return int("".join(str(n) for n in validsets[1]))
def check_pair(p1, p2):
if is_prime(concat_numbers(p1, p2)) and is_prime(concat_numbers(p2, p1)):
return True
else:
return False
def _harshad_primes(n):
return set(a for a in (n * 10 + i for i in range(1, 10))
if is_prime(a) and a < LIMIT)
def is_circ_prime(n):
digist = [int(j) for j in digits_list(n)]
return all((is_prime(int_from_digits(i)) for i in rotations_gen(digist)))
def p026():
primes_lt1000 = [i for i in range(1, 1000) if is_prime(i)]
cycles = [num_cycles(p) for p in primes_lt1000]
return primes_lt1000[cycles.index(max(cycles))]
def test_is_prime():
"""
"""
assert all(is_prime(n) for n in p_lt200)