def is_truncatable(prime):
if prime < 10:
return False
rtl = [int(str(prime)[:i]) for i in xrange(len(str(prime))) if i > 0 and i < len(str(prime))]
ltr = [int(str(prime)[i:]) for i in xrange(len(str(prime))) if i > 0 and i < len(str(prime))]
truncated = sorted(rtl + ltr, reverse=True)
for n in truncated:
if not is_prime(n):
return False
print 'OK', prime, rtl, ltr
return True
def pandigital_prime_generator(n):
if n > 7:
raise Exception('Invalid pandigital prime length')
for end in [3, 7, 9]:
digits = range(1, n + 1)
if end not in digits:
continue
digits.remove(end)
for start in sorted(permutations(digits, len(digits)), reverse=True):
number = int(''.join([str(i) for i in start] + [str(end)]))
if is_prime(number):
yield number
def main():
size = 1
diagonals = 0
primes = 0
for corners in spiral_corners_generator():
diagonals = diagonals + len(corners)
primes = primes + len([c for c in corners if is_prime(c)])
pct = primes / float(diagonals) * 100
if size > 7 and pct < 10.0:
break
size = size + 2
print 'Side Length: {0}, Percentage: {1}'.format(size, pct)
def main():
MIN = 2
MAX = 10000
sums = {}
amicable = []
i = MIN
while i < MAX:
if not is_prime(i):
s = sum(proper_divisors(i))
sums[i] = s
if s in sums and i == sums[s] and i != s:
print i, s, sums[s]
amicable.append(i)
amicable.append(s)
i = i + 1
print 'Sum of amicable numbers less than {0}: {1}'.format(MAX, sum(amicable))
def main():
MIN = 2
MAX = 10000
sums = {}
amicable = []
i = MIN
while i < MAX:
if not is_prime(i):
s = sum(proper_divisors(i))
sums[i] = s
if s in sums and i == sums[s] and i != s:
print i, s, sums[s]
amicable.append(i)
amicable.append(s)
i = i + 1
print 'Sum of amicable numbers less than {0}: {1}'.format(
MAX, sum(amicable))
def main():
MAX = 1000000
circular_primes = []
print 'Searching for circular primes for p < {0}...'.format(MAX)
for prime in prime_generator():
if prime >= MAX:
break
try:
# Ensure the prime *can* be circular
if prime > 9:
for c in [n for n in str(prime) if n not in ['1', '3', '7', '9']]:
raise NotCircular()
# Check all permutations
for rotation in cyclic_rotation(prime):
if not is_prime(rotation):
raise NotCircular()
circular_primes.append(prime)
except NotCircular:
pass
# Clear all permutations from the list?
print 'Circular Primes ({0}): {1}'.format(len(circular_primes), circular_primes)