def isTruncPrime(n):
divisor = 1
# Check first digit is prime
while True:
trunc = n // divisor
if trunc <= 0: break
if trunc == 1 or not isPrime(trunc): return False
divisor *= 10
while (n % divisor) > 0:
trunc = n % divisor
if trunc == 1 or not isPrime(n % divisor): return False
divisor /= 10
return True
def hasCriteria(n):
limit = int(sqrt(n // 2))
for dSq in [2 * i**2 for i in xrange(limit, 0, -1)]:
diff = n - dSq
if diff == 1 or isPrime(diff):
return True
return False
def challenge041():
# loop through number of digits
highest = 0
for n in [4, 7]:
chars = string.join([str(c) for c in xrange(1, n + 1)], "")
for potential in [int(p) for p in permutate(chars) if isPrime(int(p))]:
if potential > highest: highest = potential
return highest
def challenge046():
n = 3
while True:
# Find doubled squares lower than n
if not hasCriteria(n):
return n
n += 2
while n == 1 or isPrime(n): n += 2
def challenge027():
limit = 999
aMax = 0
bMax = 0
maximum = 1
bS = list(sievedPrimes(limit + 1))
for b in bS:
for a in xrange(-b, limit + 1):
n = 1
while True:
f = n * (n + a) + b
if not isPrime(f): break
n += 1
if n > maximum:
maximum = n
aMax = a
bMax = b
return aMax * bMax