def amount_of_circular_primes(lim):
pl = Prime()
pl.up_to(lim)
circular_primes = pl.sequence[:4]
for p in pl.sequence[4:-1]:
if is_circular_prime(p, pl):
circular_primes.append(p)
return len(circular_primes)
def get_largest_pandigital_prime():
pl = Prime()
combis = []
for n in xrange(2, 10):
combis.extend(permutations(range(1, n + 1), n))
combis = map(lambda x: int(''.join(map(str, x))), combis)
for n in combis[::-1]:
if pl.is_prime(n):
return n
def divisible_by_all_lower(max_divisor):
""" Return the number that is divisible by all numbers lower than the
max_divisor
"""
smallest = 1
pl = Prime()
prime_divisors = pl.up_to(max_divisor)
for p in prime_divisors:
temp = p
while temp <= max_divisor:
temp *= p
smallest *= p
return smallest
def get_abundant_numbers(n):
pl = Prime()
abundant = []
for i in xrange(12, n):
if i < proper_divisor_sum(i, pl):
abundant.append(i)
return abundant
def sum_of_amicable_numbers(n):
pl = Prime()
amicable_sum = 0
for i in xrange(2, n):
divisor_sum = d(i, pl)
if divisor_sum < i and divisor_sum > 0 and d(divisor_sum, pl) == i:
amicable_sum += divisor_sum + i
return amicable_sum
def sum_of_truncatable_primes():
pl = Prime()
truncatable_primes = []
pl.up_to(10)
while len(truncatable_primes) < 11:
if is_truncatable_prime(pl.sequence[-1], pl):
print pl.sequence[-1]
truncatable_primes.append(pl.sequence[-1])
pl.find_next()
return sum(truncatable_primes)
def find_prime(n):
ps = Prime()
return ps.up_to_element(n)[-1]
def first_triangle_divisors(n):
tri = Triangle()
pl = Prime()
while get_amount_of_divisors(pl, tri.sequence[-1]) < n:
tri.find_next()
return tri.sequence[-1]
def sum_of_primes_up_to(n):
pl = Prime()
return sum(pl.up_to(n))
def find_prime(n):
ps = Prime()
return ps.up_to_element(n)[-1]
def largest_primefactor(n):
ps = Prime()
return ps.get_prime_factors(n)[-1]
def largest_primefactor(n):
ps = Prime()
return ps.get_prime_factors(n)[-1]