Testing for prime

Probable primes

Fermat's little theorem tells us that

xp mod p = x

if p is prime for x<p

The converse is that if

xp mod p ≠ x

the p is not prime

Verify this by trying prime and non-prime values for p. You can can generate prime numbers from https://bigprimes.org/

document.body.append(
  mkInput('p','101'),
  mkInput('m','3'),
  $m('button',{onclick:function(){
    document.getElementById('result').value =
      pow(getbig('m'),getbig('p'),getbig('p'));
  }},`m<sup>p</sup> mod p`),
  $m('input',{id:'result'})
);

//raise n to the power e, modulo m
function pow(n,e,m){
  if (e<=0) return 1n;
  let r = pow(n,e/2n,m);
  return (r*r*(e%2n===1n?n:1n))%m;
}

//Create an element with tagname and properties
//children can be a string (innerHTML) or a list of elements
function $m(tag,prop,children){
  let ret = document.createElement(tag);
  for(let k in prop)
    ret[k] = prop[k];
  if (typeof(children)==='string')
    ret.innerHTML = children;
  if (Array.isArray(children))
    for(let c of children)
      ret.append(c);
  return ret;
}
//Get the value in element with id, convert it to a BigInt
function getbig(id){return BigInt(document.getElementById(id).value)}
//Return a div containing label and input. id is shown in the label
function mkInput(id,value){
  return $m('div',{},[$m('label',{},id),$m('input',{id,value})]);  
}