def p49():
primes_list = primes2.PrimeList()
primes_list.sieve(10000)
# Group together all primes in the same permutation group
permutations = {}
for prime in primes_list.get_primes_in(range(1000, 10000)):
prime_sorted_digits = tuple(sorted(str(prime)))
if prime_sorted_digits in permutations:
permutations[prime_sorted_digits].append(prime)
else:
permutations[prime_sorted_digits] = [prime]
# Keep only those with at least three primes
permutations = {
sorted_digits: primes
for sorted_digits, primes in permutations.items() if len(primes) >= 3
}
# Get arithmetic sequences of length 3
progressives = []
for primes in permutations.values():
# Pick all prime triplets
for combo in combinations(primes, 3):
#Check for progression
if combo[2] - combo[1] == combo[1] - combo[0]:
progressives.append(combo)
#There should be two sequences
assert len(progressives) == 2
# Remove known sequence
progressives.remove((1487, 4817, 8147))
the_seq = progressives[0]
return ''.join(str(prime) for prime in the_seq)
def p41():
MAX_NUM = 7654321
prime_list = primes2.PrimeList()
prime_list.sieve(MAX_NUM)
max_prime_pandigital = 0
for prime in prime_list.get_primes_in(generic.grange(MAX_NUM, -1)):
if ''.join(sorted(str(prime))) == '1234567':
max_prime_pandigital = prime
break
return max_prime_pandigital
def p46():
primes = primes2.PrimeList()
for odd in generic.grange(35, 2):
if primes.is_prime(odd):
continue
for psquare in range(1, math.floor(math.sqrt((odd - 3) / 2)) + 1):
square = 2 * psquare**2
if primes.is_prime(odd - square):
break
else:
return odd
def p35():
prime_list = primes.PrimeList()
prime_list.sieve(1000000)
number = 1 #NOTE: 2 is blocked out by (***)
for prime in prime_list.get_primes():
if prime >= 10**6:
break
#(***)
if any(x in str(prime) for x in ["0", "2" ,"4", "6", "8"]):
continue
for rotation in integers.get_rotations(prime):
if not prime_list.is_prime(rotation):
break
else:
#Did not break => They are all prime
number += 1
return number
Find the sum of the only eleven primes that are both truncatable from
left to right and right to left.
NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
Answer: 748317
"""
"""Thoughts:
Note 379 is not a truncatable prime even though it is from 3797.
"""
import utility.primes2 as p33
pl = p33.PrimeList()
def get_truncates(prime):
#Remove from right
str_prime = str(prime)
if not pl.is_prime(int(str_prime[-1]))\
or not pl.is_prime(int(str_prime[0])):
return None
truncated_primes = []
#Truncate from right first
for i in range(1, len(str_prime)-1):
new_prime = int(str_prime[:-i])
if not pl.is_prime(new_prime):
break
else:
def setUp(self):
self.prime_list = primes.PrimeList()