def is_prime_pair(prime1, prime2):
prime1 = str(prime1)
prime2 = str(prime2)
if is_prime(int(prime1 + prime2)) and is_prime(int(prime2 + prime1)):
return True
else:
return False
def truncate_prime(num):
num = str(num)
for i in range(len(num)):
if not is_prime(int(num[i:])):
return False
for i in range(len(num), 0, -1):
if not is_prime(int(num[:i])):
return False
return True
def check_num(num):
num = str(num)
for x in range(0, len(num)):
left = num[x:len(num)]
right = num[0:x + 1]
if not is_prime(int(left)) or not is_prime(int(right)):
return False
return True
def find_circular_primes():
# Start a 1 due to the edge case of 2 being prime
total = 1
for x in range(3, 1000000, 2):
if is_prime(x):
rotations = convert_to_rotations(x)
total += 1 if len([y for y in rotations
if is_prime(int(y))]) == len(rotations) else 0
return total
def is_circular_prime(num): num = str(num) length = len(num) for i in range(length): if not is_prime(int(num[i:]+num[:i])): return False return True
def find_prime(num):
prime_list = []
n = 1
while (len(prime_list) != num):
n += 1
if is_prime(n):
prime_list.append(n)
return prime_list[-1]
def truncatable_from_left(prime):
prime = str(prime)
for i in range(len(prime)):
if is_prime(int(prime[i:])):
continue
else:
return False
return True
def truncatable_from_right(prime):
prime = str(prime)
for i in range(len(prime), 0, -1):
if is_prime(int(prime[:i])):
continue
else:
return False
return True
def is_circular_prime(n):
p = 2 * str(n)
for i in range(len(str(n))):
new_prime = p[i:i + len(str(n))]
if is_prime(int(new_prime)):
continue
else:
return False
return True
def find_pandigital_prime():
largest = 0
for x in range(1, 10):
string = ''.join([str(y) for y in range(1, x + 1)])
perms = [int(''.join(z)) for z in permutations(string)]
for p in perms:
if p > largest and is_prime(p):
largest = p
return largest
def find_truncatable_primes():
primes = []
# Primes below 7 aren't included so start from the next odd number
step = 9
while len(primes) < 11:
if is_prime(step) and check_num(step):
primes.append(step)
step += 2
return sum(primes)
def consecutive_sum(limit):
primes = get_primes(limit)
most_number_elements = 0
for i in tqdm(range(len(primes))):
new_primes = primes[i:]
for j in range(len(new_primes)):
no_elements = len(new_primes[:j])
prime_sum = sum(new_primes[:j])
if prime_sum >= limit:
break
if no_elements > most_number_elements and is_prime(prime_sum):
most_number_elements = no_elements
highest_prime_sum = prime_sum
return highest_prime_sum, most_number_elements
# coding: utf-8
# 050_consecutive_prime_sum.py
from lib.primes import is_prime
primes = []
for i in range(2, 1000000):
if is_prime(i):
primes.append(i)
records = {}
n = 0
p = 1
while (n + p < len(primes)):
# print(n+p)
total = 0
length = 0
key_list = list(records.keys())
for i in range(p):
total += primes[n + i]
length += 1
if total < 1000000:
p += 1
if is_prime(total):
if length in key_list:
if records[length] < total:
records[length] = total
else:
# coding: utf-8
# 058_spiral_primes.py
from lib.primes import is_prime
spiral_list = [1]
n = 1
plus = 2
i = 0
count = 0
while (True):
value = spiral_list[i] + plus
spiral_list.append(value)
i += 1
if i % 4 == 0:
for num in spiral_list[-4:]:
if is_prime(num):
count += 1
result = count / i
print(result)
if result >= 0.1:
n += 2
plus += 2
else:
print(n)
break
def get_prime_length(a, b):
n, consequtive = 0, list()
while is_prime(quadratic_expression(n, a, b)):
consequtive.append(n)
n += 1
return len(consequtive)
# coding: utf-8
# 005_smallest_multiple.py
from lib.primes import is_prime
x = 1
for i in range(2, 21):
if is_prime(i):
x *= i
def find_smallest(num):
for i in range(1, 21):
if num % i != 0:
return False
return True
x += 10 # u'20으로 나누어 지려면 끝 자리가 20이여야 하기때문 x=9699690
while (True):
# print(x)
if find_smallest(x):
print(x)
break
else:
x += 20
# coding: utf-8
# 069_totient_maximum.py
# 수학&코딩 블로그 참조....
from lib.primes import is_prime
primes_list = [i for i in range(2, 101) if is_prime(i)]
n = 1
for x in range(len(primes_list)):
n *= primes_list[x]
if n > 1000000:
break
print(n)
# coding: utf-8
# 070_totient_permutation.py
from lib.primes import is_prime
from lib.totient import phi
def is_permutation(num1, num2):
return sorted(list(str(num1))) == sorted(list(str(num2)))
n = 9999999
while (True):
print(n)
if is_prime(n) and is_permutation(phi(n), n):
print(n)
break
n -= 1
# coding: utf-8
# pandigital_prime.py
from itertools import permutations
from lib.primes import is_prime
def make_pandigital(num):
l = [i for i in range(1, num + 1)]
permut_list = list(permutations(l, ))
result_list = []
for permutation in permut_list:
string = ''
for num in permutation:
string += str(num)
result_list.append(int(string))
return result_list
pandigital_list = make_pandigital(7)
pandigital_list.sort()
pandigital_list.reverse()
for pandigital in pandigital_list:
if is_prime(pandigital):
print(pandigital)
break
def sum_prime(num):
result = 2
for i in range(3, num, 2):
if is_prime(i):
result += i
return result