def truncatable(n):
left = str(n)
right = str(n)
while left != "":
if not is_prime(int(left)):
return False
left = left[1:]
while right != "":
if not is_prime(int(right)):
return False
right = right[:-1]
return True
def test_seq(n):
for x in range(0,3):
seq_term = guess + x * seq_len
print(seq_term)
if not is_permutation(seq_term, guess) and not is_prime(seq_term):
print("hello")
break
elif x == 2:
return int(str(guess) + str(guess + seq_len) + str(guess + 2 * seq_len))
def solve():
primes = [2]
guess = 3
while True:
if is_prime(guess):
primes.append(guess)
elif not sum_prime_twice_square(guess, primes):
return guess
guess += 2
def solve():
counter = 1
nat = 1
while(counter < 10001):
nat = nat + 2
if is_prime(nat):
counter = counter + 1
return nat
def solve():
for guess in range(1488,10000): # checked in testing that it's not before 1487
for seq_len in range(1,9999):
if guess + 2 * seq_len > 9999:
break
for x in range(0,3):
seq_term = guess + x * seq_len
if not is_permutation(seq_term, guess) or not is_prime(seq_term):
break
elif x == 2:
return int(str(guess) + str(guess + seq_len) + str(guess + 2 * seq_len))
def solve():
greatest = 0
for a in range(-1000, 1000):
for b in range(-1000, 1000):
n = 0
while is_prime(n ** 2 + a * n + b):
n = n + 1
if n > greatest:
greatest = n
best_a = a
best_b = b
return best_a * best_b
def solve():
best_case = '987654321' # 9 digit pandigital would be ideal
while best_case != '':
guess_perms = sorted([int(''.join(p)) for p in permutations(best_case)], reverse = True) # find all pandigitals
for guess in guess_perms:
if is_pandigital(guess, len(best_case)) and is_prime(guess):
return guess
else:
guess -= 1
best_case = best_case[1:] # truncate if we give up on this many digits
def primes_below(n):
total = 2
for x in xrange(3, n, 2):
if is_prime(x):
total = total + x
return total
def all_rotations_prime(n):
for x in rotations(n):
if not is_prime(x):
return False
return True
