This JavaScript function generates random number strings that pass the Luhn checksum, the test that credit card numbers must conform to. It assumes there is an HTML radio input to indicate which company issued the card. This code is from my webpage here: http://bradconte.com/cc_generator.html.

Credit Card Generator

// Copyright (c) 2015, Brad Conte (http://bradconte.com)
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//     * Redistributions of source code must retain the above copyright
//       notice, this list of conditions and the following disclaimer.
//     * Redistributions in binary form must reproduce the above copyright
//       notice, this list of conditions and the following disclaimer in the
//       documentation and/or other materials provided with the distribution.
//     * Neither the name of the <organization> nor the
//       names of its contributors may be used to endorse or promote products
//       derived from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
// ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
// WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
// DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE FOR ANY
// DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
// (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
// LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
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/**
 * @param integer type 0 = Visa, 1 = Mastercard, 2 = American Express, 3 = Discover
 * @param integer visalength 0 = 13, 1 = 16
 * @return string
 */
var cc_gen = function (type, visalength = 1) {
	var pos;
	var str = new Array(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
	var sum = 0;
	var final_digit = 0;
	var t = 0;
	var len_offset = 0;
	var len = 0;
	var issuer;

	//
	// Fill in the first values of the string based with the specified bank's prefix.
	//

	// Visa
	if (type == 0) {
		str[0] = 4;
		pos = 1;
		if (visalength == 1) {
			len = 16;
		}
		else {
			len = 13;
		}
	}
	// Mastercard
	else if (type == 1) {
		str[0] = 5;
		t = Math.floor(Math.random() * 5) % 5;
		str[1] = 1 + t;	  // Between 1 and 5.
		pos = 2;
		len = 16;
	}
	// American Express
	else if (type == 2) {
		str[0] = 3;
		t = Math.floor(Math.random() * 4) % 4;
		str[1] = 4 + t;	  // Between 4 and 7.
		pos = 2;
		len = 15;
	}
	// Discover
	else if (type == 3) {
		str[0] = 6;
		str[1] = 0;
		str[2] = 1;
		str[3] = 1;
		pos = 4;
		len = 16;
	}
	else {
		console.error('Please select a type between 0 and 4.');
	}

	//
	// Fill all the remaining numbers except for the last one with random values.
	//

	while (pos < len - 1) {
		str[pos++] = Math.floor(Math.random() * 10) % 10;
	}

	//
	// Calculate the Luhn checksum of the values thus far.
	//

	len_offset = (len + 1) % 2;
	for (pos = 0; pos < len - 1; pos++) {
		if ((pos + len_offset) % 2) {
			t = str[pos] * 2;
			if (t > 9) {
				t -= 9;
			}
			sum += t;
		}
		else {
			sum += str[pos];
		}
	}

	//
	// Choose the last digit so that it causes the entire string to pass the checksum.
	//

	final_digit = (10 - (sum % 10)) % 10;
	str[len - 1] = final_digit;

	// Output the CC value.
	t = str.join('');
	t = t.substr(0, len);
	return t;
}

cc_gen(Math.floor(Math.random() * 4));