def memo_is_prime(n):
if n in primes:
return True
if is_prime(n):
primes.add(n)
return True
return False
# -*- coding: utf-8 -*-
"""
Created on Mon Oct 30 15:36:05 2017
@author: Edward
We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
What is the largest n-digit pandigital prime that exists?
"""
import itertools
from myutils import is_prime
largest = 0
for i in range(2, 11):
vals = [i for i in range(1, i)]
for permute in itertools.permutations(vals):
val = sum([a * 10**b for b, a in enumerate(permute[::-1])])
if is_prime(val):
if val > largest:
largest = val
print(largest)
# -*- coding: utf-8 -*-
"""
Created on Mon Oct 30 21:05:29 2017
@author: Edward
The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.
What 12-digit number do you form by concatenating the three terms in this sequence?
"""
from myutils import is_prime
primes = set()
for i in range(1001, 10000, 2):
if is_prime(i):
primes.add(i)
for prime in primes:
for i in range(1, 10000 - prime):
if prime + i in primes and prime + 2 * i in primes and sorted(
str(prime + i)) == sorted(str(prime)) and sorted(
str(prime + 2 * i)) == sorted(str(prime)):
print(prime, prime + i, prime + 2 * i, i)
ind = 1
next_size = 3
while True:
num_vals = (next_size - 2) * 4 + 4
values = list(
range(ind + next_size - 1, num_vals + ind + 1, next_size - 1))
ind = values[-1]
next_size += 2
yield values
num_primes = 0
total = 1
for size, vals in zip(range(1, 100001, 2), triangle_generator()):
if vals == [1]:
continue
total += len(vals)
for v in vals:
if is_prime(v):
num_primes += 1
if num_primes / total < 0.1:
print(size)
break
