def main():
primes = [2, 3]
consecutives = []
number_of_consecutives = 4
index = 3
while len(consecutives) < number_of_consecutives:
index += 1
if is_prime(index):
primes.append(index)
consecutives = []
continue
prime_factors = set()
factored = index
for prime in primes:
while factored % prime == 0 and factored and len(
prime_factors) < number_of_consecutives + 1:
prime_factors.add(prime)
factored /= prime
if not factored or len(prime_factors) > number_of_consecutives - 1:
break
if len(prime_factors) == number_of_consecutives:
consecutives.append(index)
else:
consecutives = []
print consecutives
def main():
primes = [2, 3]
consecutives = []
number_of_consecutives = 4
index = 3
while len(consecutives) < number_of_consecutives:
index += 1
if is_prime(index):
primes.append(index)
consecutives = []
continue
prime_factors = set()
factored = index
for prime in primes:
while factored % prime == 0 and factored and len(prime_factors) < number_of_consecutives + 1:
prime_factors.add(prime)
factored /= prime
if not factored or len(prime_factors) > number_of_consecutives - 1:
break
if len(prime_factors) == number_of_consecutives:
consecutives.append(index)
else:
consecutives = []
print consecutives
def is_truncatable_prime(num):
for i in ['0', '4', '6', '8']:
if i in str(num):
return False
for i in ['2', '5']:
if i in str(num)[1:]:
return False
if not is_prime(num):
return False
for idx in range(len(str(num)) - 1):
if not is_prime(int(str(num)[idx+1:])):
return False
for idx in range(len(str(num)) - 1):
if not is_prime(int(str(num)[0:-1*idx-1])):
return False
return True
def is_truncatable_prime(num):
for i in ['0', '4', '6', '8']:
if i in str(num):
return False
for i in ['2', '5']:
if i in str(num)[1:]:
return False
if not is_prime(num):
return False
for idx in range(len(str(num)) - 1):
if not is_prime(int(str(num)[idx + 1:])):
return False
for idx in range(len(str(num)) - 1):
if not is_prime(int(str(num)[0:-1 * idx - 1])):
return False
return True
def main():
primes = [i for i in range(1000, 10000) if is_prime(i)]
primes_set = set(primes)
found_lists = []
while len(found_lists) < 2:
first_prime = primes[0]
primes.pop(0)
for p in primes:
prime_list = [first_prime]
diff = p - first_prime
if p + diff in primes_set:
prime_list += [p, p + diff]
if is_list_of_permutations(prime_list):
found_lists.append(prime_list)
print "".join([str(i) for i in found_lists[1]])
def main():
primes = set()
index = 1
found_composite = 0
while not found_composite:
index += 2
if is_prime(index):
primes.add(index)
continue
correct_proposition = False
for prime in primes:
square = (index - prime) / 2.0
if int(square) == square and int(sqrt(square)) == sqrt(square):
correct_proposition = True
if not correct_proposition:
found_composite = index
print found_composite