Sandwich Primes - ( the term I coined ;)), inspired by this post by Pat Ballew https://www.linkedin.com/posts/pat-ballew-5b1935102_mathfacts-activity-6769661475427491841-F4n-, are primes p, such that 1p1, 3p3, 7p7 and 9p9 are all primes.
This code finds all sandwich primes in the set of first 10000 primes.
// adapted from https://stackoverflow.com/a/15471749/983091
var eratosthenes = function(n) {
// Eratosthenes algorithm to find all primes under n
var array = [], upperLimit = Math.sqrt(n), map = {}, output = [];
// Make an array from 2 to (n - 1)
for (var i = 0; i < n; i++) {
array.push(true);
}
// Remove multiples of primes starting from 2, 3, 5,...
for (var i = 2; i <= upperLimit; i++) {
if (array[i]) {
for (var j = i * i; j < n; j += i) {
array[j] = false;
}
}
}
// All array[i] set to true are primes
for (var i = 2; i < n; i++) {
if(array[i]) {
map[i]=true;
output.push(i);
}
}
return [output, map];
};
let [primes, pMap] = eratosthenes(1000000)
for (let i = 0; i < 10000; i++) {
let p = primes[i]
if (pMap[+('1' + p + '1')] && pMap[+('3' + p + '3')] && pMap[+('7' + p + '7')] && pMap[+('9' + p + '9')]) {
console.log(p)
}
}
console.log('done')
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