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/**

* Problem 35 - Circular primes

*

* @see {@link https://projecteuler.net/problem=35}

*

* The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.

* There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.

* How many circular primes are there below one million?

*

* @author ddaniel27

*/

import { sieveOfEratosthenes } from '../Maths/SieveOfEratosthenesIntArray'

function problem35 (n) {

if (n < 2) {

throw new Error('Invalid input')

}

// Get a list of primes without 0, 2, 4, 5, 6, 8; this discards the circular primes 2 & 5

const list = sieveOfEratosthenes(n).filter(prime => !prime.toString().match(/[024568]/))

const result = list.filter((number, _idx, arr) => {

const str = String(number)

for (let i = 0; i < str.length; i++) { // Get all rotations of the number

const rotation = str.slice(i) + str.slice(0, i)

if (!arr.includes(Number(rotation))) { // Check if the rotation is prime

return false

}

}

return true // If all rotations are prime, then the number is circular prime

})

return result.length + 2 // Add 2 to the result because the circular primes 2 & 5 were discarded

}

export { problem35 }