def check_concat_prime(*args):
for i in range(len(args)):
for j in range(i+1, len(args)):
if not is_prime(int(str(args[i])+str(args[j]))) \
or not is_prime(int(str(args[j])+str(args[i]))):
return False
return True
def check_concat_prime(*args):
for i in range(len(args)):
for j in range(i + 1, len(args)):
if not is_prime(int(str(args[i])+str(args[j]))) \
or not is_prime(int(str(args[j])+str(args[i]))):
return False
return True
def prime_cluster(rule, number):
rule = int(rule)
cluster = [number + rule * i for i in range(10)]
count = sum(is_prime(i) for i in cluster)
if count >= 8:
print(count)
for item in cluster:
if is_prime(item):
print(item)
return count
def prime_cluster(rule, number):
rule = int(rule)
cluster = [number + rule * i for i in range(10)]
count = sum(is_prime(i) for i in cluster)
if count >= 8:
print(count)
for item in cluster:
if is_prime(item):
print(item)
return count
def get_prime_pan(curr, min_num, digits_left):
for perm in permutations(digits_left):
num = int(''.join(perm))
if num <= min_num:
continue
if is_prime(num):
pan_primes = tuple(curr) + (num, )
# print(pan_primes)
pan_prime_sets.append(pan_primes)
def get_prime_pan(curr, min_num, digits_left):
for perm in permutations(digits_left):
num = int(''.join(perm))
if num <= min_num:
continue
if is_prime(num):
pan_primes = tuple(curr) + (num, )
# print(pan_primes)
pan_prime_sets.append(pan_primes)
def next_harshads(harshad_tuple):
num_orig = harshad_tuple[0]
harshads = []
for d in range(10):
num = num_orig * 10 + d
div, mod = divmod(num, digit_sum(num))
if mod == 0:
harshads.append((num, is_prime(div)))
return harshads
def get_prime(min_num, digits_left):
digits_left_len = len(digits_left)
min_size_len = len(str(min_num))
for i in range(min_size_len, digits_left_len // 2 + 1):
for comb in combinations(digits_left, i):
for perm in permutations(comb):
num = int(''.join(perm))
if num <= min_num:
continue
if is_prime(num):
yield num
def get_prime(min_num, digits_left):
digits_left_len = len(digits_left)
min_size_len = len(str(min_num))
for i in range(min_size_len, digits_left_len//2+1):
for comb in combinations(digits_left, i):
for perm in permutations(comb):
num = int(''.join(perm))
if num <= min_num:
continue
if is_prime(num):
yield num
def main():
N = 25
composites = []
for n in range(3, 1000000, 2):
if n % 5 == 0 or is_prime(n):
continue
a_n = A(n)
if (n-1) % a_n == 0:
# print(n, a_n)
composites.append(n)
if len(composites) >= N:
break
print(sum(composites))
def main():
N = 25
composites = []
for n in range(3, 1000000, 2):
if n % 5 == 0 or is_prime(n):
continue
a_n = A(n)
if (n - 1) % a_n == 0:
# print(n, a_n)
composites.append(n)
if len(composites) >= N:
break
print(sum(composites))
def check_concat_prime_against(old, new):
for i in old:
if not is_prime(int(str(i)+str(new))) \
or not is_prime(int(str(new)+str(i))):
return False
return True
def harshad_prime(num):
return [num * 10 + d for d in [1, 3, 7, 9] if is_prime(num * 10 + d)]
def check_concat_prime_against(old, new):
for i in old:
if not is_prime(int(str(i)+str(new))) \
or not is_prime(int(str(new)+str(i))):
return False
return True
