This article is rated C-class on Wikipedia's content assessment scale.
It is of interest to the following WikiProjects:

Mathematics Low‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Low	This article has been rated as Low-priority on the project's priority scale.

Computing

	This article is within the scope of WikiProject Computing, a collaborative effort to improve the coverage of computers, computing, and information technology on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.ComputingWikipedia:WikiProject ComputingTemplate:WikiProject ComputingComputing articles
???	This article has not yet received a rating on the project's importance scale.
	This article has been automatically rated by a bot or other tool because one or more other projects use this class. Please ensure the assessment is correct before removing the `\|auto=` parameter.

Is this algorithm correct?

According to [1], 3170092 is also a valid number.

Using the algorithm here, that becomes:

i	n_i	p(i,n_i)	previous c	new c = d(c,p(i,n_i))
0	2	2	0	2
1	9	4	2	1
2	0	5	1	6
3	0	8	6	3
4	7	8	3	6
5	1	2	6	9
6	3	3	9	6

Which one is incorrect? The wikiarticle? The other article? The fact that 3170092 is a valid number? Or have I made a mistake?

As best I can tell, the Marist College article you cited is wrong. The position-based permutation which Verhoeff settled on (the p table) is not a simple exponential of the group multiplication (the d table), as the article you found claims.

My understanding (from the first reference in the Wikipedia article) is that Verhoeff experimented with many different permutations before coming up with one that worked particularly well. A simple exponential permutation would actually be atrociously bad, since multiplication in the dihedral group contains two cycles of period 2 — namely, (14) and (23) — and one cycle of period 1 — namely, (0).

Richwales 20:50, 24 September 2006 (UTC)[reply]

195.224.169.69 19:29, 26 September 2006 (UTC) Thanks for the information.[reply]

(A few years later...)

3170092 is given as an example of valid number in Kirtland, Joseph (2001): Identification Numbers and Check Digit Schemes (see the exact reference in the article).

From a quick superficial reading, it looks like Kirtland and the Wikipedia article actually use 2 different variants of the Verhoeff algorithm, so no wonder a number accepted by Kirtland is refused by Wikipedia. The difference lies in table p: while the Wikipedia article uses powers of permutation (1 5 8 9 4 2 7 0)(3 6), Kirtland uses powers of (0) (1 4) (2 3) (5 6 7 8 9). (Also, they might apply the powers in a different direction to the original digits: right-to-left for Kirtland, left-to-right for Wikipedia, I haven't checked.) The algorithm in the Wikipedia article seems to be the one in use by the German Bundesbank between 1990 and (2002?) for their banknote serial numbers. (Actually, Kirtland also does mention the German Bundesbank and its permutation, in a final short note.) --FvdP (talk) 20:50, 20 August 2012 (UTC)[reply]

Even more years later ... I can confirm Verhoeff evaluations a great number of different permutations, and I added that to the main article with reference to this particular permutation (1 5 8 9 4 2 7 0)(3 6). The original paper has sophisticated measurements for different permutations. According to my understanding, 3170099 is correct for the 'canonical' permutation as given in the Wiki article and all of the implementations I've seen (from the links on main article). The Marist College page ([2]) uses a different permutation, as noted by FvpP above, which will give you a different answer. I'm afraid I don't have access to the Kirtland book to see what he says there. 217.155.120.113 (talk) 20:11, 23 March 2014 (UTC)[reply]

I don't understand the following description:

"The involved nature of the Verhoeff check might especially be seen as a drawback if the client applications within a system need to explicitly identify ID's that fail the check digit test. If it is sufficient for a client to look up each ID in a master database and report malformed values as "not found," then only the piece of the system that issues new ID's needs to know how to do the Verhoeff calculations, and the complexity issue is mitigated."

Can someone more knowledgable try to explain it better? The first sentence sounds like the reason why to use a check digit in the first place. 193.12.151.160 (talk) —Preceding comment was added at 16:27, 7 March 2008 (UTC)[reply]

I added some explanation which I hope will take care of this issue. The point is that if all a client application needs to be told is that a given ID is not found in the system, there is no need for the client app to do the check-digit calculations itself; it will simply do a lookup using the malformed ID, and it won't match anything. However, if it is decided that a client application needs to be able to explicitly say that a given ID has failed the check-digit test and must have been garbled somehow, then the client would naturally need to have the necessary smarts to do the check-digit calculations on the ID before trying to do a lookup. Richwales (talk) 19:55, 7 March 2008 (UTC)[reply]

In general you might also care to do user validation of input as early as possible, and you might care to give different error messages when you a) see the user has made a typo, or b) there actually isn't such a record. In practice, for example, you might check the checksum in javascript on a web input page before sending the form to a server. Also, in practice there's not very much difference in the difficulty of implementing any of the checksum algorithms, nor their computational complexity. Hope that's of some use. 217.155.120.113 (talk) 20:11, 23 March 2014 (UTC)[reply]

This article is incomplete

This article is incomplete please add the complete algorithm either in pseudocode or the steps list. — Preceding unsigned comment added by 2806:106E:B:AEBA:26EB:3B05:6D18:7C96 (talk) 23:05, 3 December 2023 (UTC)[reply]

Better Example?

Not sure 236 is a great example because 236 is ALSO a Verhoeff number. 150.143.239.141 (talk) 14:07, 9 April 2024 (UTC)[reply]

Error in example?

In the Description, it says 'the check digit for 248 is 5'. However, this does not seem to be consistent with the definition of f and the verification given in the same section. If the number is instead 249 everything else seems to agree (also supported by https://kik.amc.nl/home/rcornet/verhoeff.html ); should it be 'the check digit for 249 is 5'? 62.63.252.68 (talk) 21:49, 28 October 2024 (UTC)[reply]