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Im nto sure what you mean by that a number is 10000 digits if theyre 10-digit numbers. But if you want to multiply numbers you can jsut do divide and multiply.

pseudocode'ish:

def multiply (a,b):
  res = 0
  while a > 1:  
    if a & 1 == 1:
      res += b
    else:
      a = a >> 1
      res *= 2
  return res

import java.util.Scanner;
public class LargeMultiply {
// main method
public static void main(String args[]) {
System.out.println("\n\t \t WELCOME TO OneArmed Blog !!! \n");
System.out.println("\t \t Multiplying 2 Large Numbers \n");
Scanner sc = new Scanner(System.in);
System.out.println("Enter 1st Number:"); //input first number
String inputA = sc.next(); // taking string input
System.out.println("Enter 2nd Number:"); //input second number
String inputB = sc.next(); // taking string input
LargeMultiply inst = new LargeMultiply();
//Object creation of class LargeMultiply
String v = inst.multiply(inputA, inputB);
// calling method multiply()
System.out.println("RESULT:");
System.out.println(v); // Output result
}
/*-- multiply method , return type String ,
2 String parameters---- */
public String multiply(String num1, String num2) {
String[] str1 = num1.split("");
//Split the number string into array with each element
// containing single digit
String[] str2 = num2.split("");
int m1 = 0;
int m2 = 0;
String[] resultStringArray = new String[str2.length];
//Initializing the resultString array which has input
// string2 in Array form with each element
//in different Index
LargeMultiply inst1 = new LargeMultiply();
//multiply every element of String2 with the String1
// using multiplySmall() method
for (int j = str2.length - 1; j > 0; j--)
resultStringArray[j] = inst1.multiplySmall(num1, str2[j]);
// call to multiplySmall() method
for (int i = num2.length() - 1; i > 0; i--) {
for (int j = 1; j <= i; j++) {
resultStringArray[j] = resultStringArray[j].concat("0");
//concat number of zeroes which are equal to the number of
//digits in 2nd number
}
}
String finalResult = "0"; // Initialize output String
for (int j = str2.length - 1; j > 0; j--) {
finalResult = inst1.add(finalResult, resultStringArray[j]);
//call to adding large numbers method
}
return finalResult; //return result
}
/*----Method to multiply a single digit to large digits----- */
public String multiplySmall(String large, String small) {
int smallInt = Integer.parseInt(small);
//String to int conversion
String[] s = large.split("");
String[] largeStringArray = new String[s.length - 1];
//Initiate a String array
//as discussed earlier split function makes
//an array which has first element “” empty
//so in order to remove that element
//we have to make another array,here it is
//largeStringArray
for (int i = 0; i < largeStringArray.length; i++) {
largeStringArray[i] = s[i + 1];
}

int[] largeInt = new int[largeStringArray.length];
//make a integer array for num1 which is considered large
for (int i = 0; i < largeStringArray.length; i++) {
largeInt[i] = Integer.parseInt(largeStringArray[i]);
//String to int conversion of every element
}
//Logic for carry
int carry = 0;
String[] resultCarry = new String[2];
//carry number represented by 2 element String array
String result = "";// result to be stored in string form
int resultInt = 0;//carry in form of integer
//int count = 0;
for (int i = largeStringArray.length - 1; i >= 0; i--) {
resultInt = largeInt[i] * smallInt + carry;
//multiplying every element of the largeInt
// with single digit integer
carry = 0;//after every multiplication carry to be made zero
if (i == 0) { // if no carry
resultInt = resultInt; // no change
} else { // If carry then
if (resultInt / 10 > 0) {
//if output on multiplying is of 2 digits
String s2 = Integer.toString(resultInt);
//convert int to String
String[] s3 = s2.split("");
// Split the Result on basis of every digit
carry = Integer.parseInt(s3[1]);
//make the first digit stored on index 1, carry
resultInt = resultInt % 10;
//keep the unit place digit of the carry
//result which is concated later
}
}
result = Integer.toString(resultInt).concat(result);
//convert unit place of result to String and concat
// it with previous results
}
return result;
//return result, which is multiplication of single
// digit number of num2 to the whole num1
}
/*----------Method to add 2 large numbers-------- */
public String add(String num1, String num2) {
char[] tempChar1 = num1.toCharArray();
//converting String num1 to character Array using
// toCharArray() function
char[] tempChar2 = num2.toCharArray();
//converting String num2 to character Array
//using toCharArray() function
char[] ch2;
char[] ch1;
//condition to check which number is longer
if (tempChar1.length > tempChar2.length) { // if 1st is larger
ch2 = tempChar1; // assign ch2 to num1
ch1 = tempChar2; // assign ch1 to num2
} else { //if second is larger
ch2 = tempChar2;// assign ch2 to num2
ch1 = tempChar1;// assign ch1 to num1
} // so always the small number gets stored in ch1
String ans = ""; //Initiating Result String, ans
int tempAns = 0;
int carry = 0;
int smallerStringIndex;
char smallerStringNumber;
smallerStringIndex = ch1.length - 1;
//represents index for smaller number
for (int i = ch2.length - 1; i >= 0; i--) {
//if index becomes negative add '0'
// at the start of smaller digit, will have no effect
if (smallerStringIndex < 0) {
smallerStringNumber = '0';
} else {
smallerStringNumber = ch1[smallerStringIndex];
}
tempAns = (smallerStringNumber + ch2[i] - 96 + carry);
// -96 the ASCII value gives actual value of the char in int
if (tempAns >= 10) {
//if there is a carry
tempAns = tempAns - 10;
//tempAns now contains the unit digit after addition
ans = tempAns + ans;
carry = 1; //assign 1 to carry
} else {
ans = tempAns + ans; //case of no carry
carry = 0;
}
smallerStringIndex--; //reduce index by 1
}
if (carry == 1) {
ans = "1" + ans;
//adding String "1" to final result if at the
//end the last digits add up to give a carry
}
return ans; //return result in String
}
}

1337 * 42