HP Prime and Numworks: Luhn Algorithm
The Luhn Algorithm: Is Your Credit Card Number Valid?
The Luhn algorithm, created by IBM scientist Hans Peter Luhn in 1954, also known as the modulus 10 algorithm, is a checksum algorithm used to check the validity certain numbers used in financial transactions, such as identification numbers and credit card numbers. The algorithm is in public domain and serves as a basic check.
The general steps of the Luhn Algorithm:
1. Starting at the rightmost digit, double every other digit (2nd digit from the rightmost digit, 4th digit from right, 6th digit from right, and so on)
2. If the digit that is doubled is at least 10, add the digits together.
Replace 10 with 1.
Replace 12 with 3.
Replace 14 with 5.
Replace 16 with 7.
Replace 18 with 9.
3. Take the sum of all the digits.
4. If the sum is a multiple of 10 (sum modulo 10 is equal to zero), the number is considered valid.
Example: 4366357
For illustration purposes, let's separate each of the digits:
4 3 6 6 3 5 7
There are 7 digits.
2nd digit from the most right: 5. Double it to 10. 1 + 0 = 1
4 3 6 6 3 1 7
4th digit from the most right: 6. Double it to 12. 1 + 2 = 3
4 3 6 3 3 1 7
6th digit from the most right: 3. Double it to 6.
4 6 6 3 3 1 7
Now add the digits: 4 + 6 + 6 + 3 + 3 + 1 + 7 = 30
10 divides into 30 evenly, or 30 mod 10 = 0. The integer 4366357 is valid according to the Luhn algorithm.
HP Prime Program: LUNH
EXPORT LUHN()
BEGIN
// Luhn Algorithm - HP Prime
// strings are used to accommodate
// string: type 2
LOCAL s,l,k,c,t,n;
INPUT({{s,[[2]]}},
"Luhn Algorithm",
{"N?"},{"Integer"});
l:=DIM(s);
k:=l;
// total
t:=0;
// loop
WHILE k>0 DO
n:=EXPR(MID(s,k,1));
IF FP((l-k)/2)==0.5 THEN
IF n≠0 THEN
n:=(2*n-1) MOD 9+1;
END;
END;
t:=t+n;
k:=k-1;
END;
// final results
IF t MOD 10==0 THEN
RETURN "VALID";
ELSE
RETURN "NOT VALID";
END;
END;
Numworks Python Script: luhn.py
from math import *
# Luhn Algorithm
# 2021-01-10 EWS
# Numworks Python
# strings are used
s=str(input('Integer? '))
l=len(s)
k=l
# total
t=0
# loop
while k>0:
n=float(s[k-1])
f=(l-k)/2
if f-int(f)==0.5:
if n!=0:
n=fmod(2*n-1,9)+1
t=t+n
k=k-1
# final results
if fmod(t,10)==0:
print("VALID")
else:
print("NOT VALID")
Examples
38348 returns NOT VALID
14956 returns NOT VALID
4382 returns VALID
Source
"Luhn algorithm" GeeksforGeeks. Noida, Uttar Pradesh. https://www.geeksforgeeks.org/luhn-algorithm/ Retrieved January 1, 2021.
"Luhn algorithm". Wikipedia. Last Updated December 23, 2020. https://en.wikipedia.org/wiki/Luhn_algorithm Retrieved January 1, 2021.
Eddie
All original content copyright, © 2011-2021. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
