# Online Lemoine’s Conjecture Demo

Lemoine’s Conjecture says any odd integer greater than 5 can be represented as the sum of an odd prime number and an even semiprime. Another statement which is suitable for programming is that 2n + 1 = p + 2q always has a solution in primes p and q (not necessarily distinct) for n > 2. This online demo will find p and q for given odd number greater than 5.

Input Odd Number Greater Than 5:

Source Code (HTML)

```Input Odd Number Greater Than 5: <input type="text" name="n"><br><br>
<button type="button" id="getLemoine">Get Lemoine’s Conjecture</button><br><br>
<textarea id="result" rows="20" cols="50"></textarea>
```

Source Code (JavaScript)

```var elmn = document.querySelector("input[name='n']");
var btn = document.querySelector("#getLemoine");
var resultElm = document.querySelector("#result");
var n = parseInt(elmn.value);
if (!Number.isInteger(n)) {
resultElm.value = "input must be integer!";
return;
}
if ( n<=5 || n%2 == 0) {
resultElm.value = "n must be greater than 5 and must be odd!";
return;
}
Lemoine(n);
});

function IsPrime(n) {
if (n<2) {
return false;
}

var i;
for (i = 2; i*i <= n; i++) {
if (n%i == 0) {return false;}
}
return true;
}

function Lemoine(n) {
var pqPairs = {};

var q;
for (q = 1; q <= n/2; q++) {
var p = n - 2*q;

if (IsPrime(p) && IsPrime(q)) {
pqPairs[p] = q;
}
}

resultElm.value = "";
for (var p in pqPairs) {
var q = pqPairs[p];
resultElm.value += (n.toString() + " = " + p.toString() + " + ( 2 * " + q.toString() + " ) \n");
}
}
```

Tested on: Chromium 65.0.3325.181 on Ubuntu 17.10 (64-bit)

References: