def p060():
familys = []
for p in tqdm(primes()):
for family in familys:
candidate = [*family, p]
if all(
is_prime(int(f'{p}{f}')) and is_prime(int(f'{f}{p}'))
for f in family):
if len(candidate) >= 4:
print(f'length:{len(candidate)}, sum:{sum(candidate):20}',
candidate)
if len(candidate) >= 5:
return
familys.append(candidate)
familys.append([p])
def prime_family(prime, digit):
members = 0
for dig in "0123456789":
next = int(prime.replace(digit, dig))
if is_prime(next) and next > 100000:
members += 1
return members == 8
def is_trunctable(n):
if not is_prime(n):
return False
else:
temp = n // 10
temp2 = n % 10
dividend = 10
while temp != 0:
if not is_prime(temp):
return False
temp = temp // 10
while dividend < n:
if not is_prime(temp2):
return False
dividend *= 10
temp2 = n % dividend
return True
def answer():
pandigitals = perms(7654321)
print(pandigitals)
final = 0
for next in pandigitals:
if is_prime(next):
final = next
break
return final
def p058():
total = 1
primes = 0
length = 1
ds = diagonals()
while primes / total >= 0.1 or primes == 0:
length += 2
for _ in range(4):
total += 1
if is_prime(next(ds)):
primes += 1
print(length)
def answer():
prime = 0
diagonals = [1]
ratio = 0.62
side = 3
while True:
square = side**2
next1 = square - (side-1)
next2 = square - (side-1)*2
next3 = square - (side-1)*3
if is_prime(next1):
prime += 1
if is_prime(next2):
prime += 1
if is_prime(next3):
prime += 1
diagonals.extend([square, next1, next2, next3])
ratio = prime / len(diagonals)
if ratio < 0.1:
break
side += 2
return side
def answer():
# Lower bound is 1487
found = 0
primes = primes_to(10000, 1487)
for a in range(len(primes)):
for b in range(a+1, len(primes)):
prime_a = primes[a]
prime_b = primes[b]
c = prime_b + (prime_b - prime_a)
if c < 10000 and is_prime(c):
if is_perm(prime_a, prime_b) and is_perm(prime_a, c):
found = str(prime_a) + str(prime_b) + str(c)
break
if found:
break
return found
def answer():
smallest = 1
proven = False
primes = [2]
while not proven:
smallest += 2
if is_prime(smallest):
primes.append(smallest)
continue
proven = True
for prime in primes:
if is_twiceSquare(smallest - prime):
proven = False
break
return smallest
def answer(n):
length = 0
longest = 0
primes = primes_to(n)
# Make a list of sums
prime_sum = [0]
for x in range(len(primes)):
prime_sum.append(prime_sum[x] + primes[x])
for a in range(len(prime_sum)):
b = a - (length + 1)
while b >= 0:
dif = prime_sum[a] - prime_sum[b]
if dif > n:
b -=1
break
if is_prime(dif):
length = a - b
longest = dif
b -=1
print("The prime is: " + str(longest) + " and consists of " + str(length) + " primes.")
def test_p060():
assert all(is_prime(p) for p in concatenate_numbers([3, 7, 109, 673]))
assert concatenating_primes([3, 7, 109, 673])
def concatenating_primes(numbers):
return all(is_prime(p) for p in concatenate_numbers(numbers))
def right_truncatable_prime(p):
return all(is_prime(n) for n in right_truncated(p))
def left_truncatable_prime(p):
return all(is_prime(n) for n in left_truncated(p))
from euler_helpers import is_prime
def circulate(n):
"""Return the list of numbers that are formed by cycling the digits of n"""
digits = list(d for d in str(n))
for cycle in range(1, len(digits) + 1):
yield int("".join(digits))
digits = digits[1:] + [digits[0]]
checked = {}
num = 0
for number in range(1, 1000001):
if number in checked:
continue
circle = list(circulate(number))
if all(is_prime(c) for c in circle):
num += len(circle)
for c in circle:
checked[c] = True
checked = sorted(checked)
print(checked)
print(len(checked))
def first_non_goldbach():
for composite in tqdm(range(33, 10**5, 2)):
if is_prime(composite):
continue
if not is_goldbach(composite):
return composite
def is_prime_set(primes):
return all(is_prime(int(str(prime[0]) + str(prime[1]))) for prime in itertools.permutations(primes, 2))
