luhn algorithm https://devstree.io/luhn-algorithm/

1.java

public class Cards {
    /**
     * Checks if the card is valid
     * 
     * @param card
     *           {@link String} card number
     * @return result {@link boolean} true of false
     */
    public static boolean luhnCheck(String card) {
        if (card == null)
            return false;
        char checkDigit = card.charAt(card.length() - 1);
        String digit = calculateCheckDigit(card.substring(0, card.length() - 1));
        return checkDigit == digit.charAt(0);
    }
    
    /**
     * Calculates the last digits for the card number received as parameter
     * 
     * @param card
     *           {@link String} number
     * @return {@link String} the check digit
     */
    public static String calculateCheckDigit(String card) {
        if (card == null)
            return null;
        String digit;
        /* convert to array of int for simplicity */
        int[] digits = new int[card.length()];
        for (int i = 0; i < card.length(); i++) {
            digits[i] = Character.getNumericValue(card.charAt(i));
        }
        
        /* double every other starting from right - jumping from 2 in 2 */
        for (int i = digits.length - 1; i >= 0; i -= 2)    {
            digits[i] += digits[i];
            
            /* taking the sum of digits grater than 10 - simple trick by substract 9 */
            if (digits[i] >= 10) {
                digits[i] = digits[i] - 9;
            }
        }
        int sum = 0;
        for (int i = 0; i < digits.length; i++) {
            sum += digits[i];
        }
        /* multiply by 9 step */
        sum = sum * 9;
        
        /* convert to string to be easier to take the last digit */
        digit = sum + "";
        return digit.substring(digit.length() - 1);
    }
    
    public static void main(String[] args)    {
        String pan1 = "37828224631000";
        System.out.println("Cards luhn calculator");
        System.out.println();
        System.out.println("Calculate check digit for: " + pan1);
        String digit = calculateCheckDigit(pan1);
        System.out.println("Check digit: " + digit);
        System.out.println();
        
        String pan2 = "4012888888881881";
        System.out.println("Validate pan number '" + pan2 + "': " + luhnCheck(pan2));
    }
    
}