def isTruncatable(num):
if not mathlib.isPrime(num):
return False
num_str = str(num)
length = len(num_str)
for i in range(1, length):
if not mathlib.isPrime(int(num_str[0:i])):
return False
for i in range(1, length):
if not mathlib.isPrime(int(num_str[i:length+1])):
return False
return True
def solve():
digits = [str(x) for x in range(1, 10)]
while len(digits) > 1:
seq = copy.deepcopy(digits)
pandigitals = [int(x) for x in mathlib.permute(seq)]
#if int(x[len(digits)-1]) % 2 != 0 and x[len(digits)-1] != '5']
# we do some optimization here, to filter the element could be divid by
# any number in range 2 to 9
optimization = []
for item in pandigitals:
op = True
for i in range(2, 10):
if item % i == 0:
op = False
break
else:
pass
if op == True:
optimization.append(item)
optimization.sort()
digits.pop()
for i in range(len(optimization)-1, -1, -1):
if mathlib.isPrime(optimization[i]):
return optimization[i]
return ''
def solve():
init, dias, primes, max_dias = 7, 13, 8, 49
while True:
ratio = primes / float(dias)
if ratio <= 0.1:
break
init += 2
for i in range(4):
max_dias += (init-1)
if mathlib.isPrime(max_dias):
primes += 1
dias += 1
return init
def solve():
primes = mathlib.getPrimes(1000000)
primesum = [0]
s = 0
count = 0
while s < 1000000:
s += primes[count]
primesum.append(s)
count += 1
terms = 1
for i in range(count):
for j in range(i + terms, count):
n = primesum[j] - primesum[i]
if (j-i>terms and mathlib.isPrime(n)):
terms, maxprime = j-i, n
return maxprime