<s>
The	O
Luhn	B-Algorithm
algorithm	I-Algorithm
or	O
Luhn	B-Algorithm
formula	I-Algorithm
,	O
also	O
known	O
as	O
the	O
"	O
modulus	B-Algorithm
10	I-Algorithm
"	O
or	O
"	O
mod	B-Algorithm
10	I-Algorithm
"	O
algorithm	O
,	O
named	O
after	O
its	O
creator	O
,	O
IBM	O
scientist	O
Hans	O
Peter	O
Luhn	B-Algorithm
,	O
is	O
a	O
simple	O
checksum	B-Algorithm
formula	O
used	O
to	O
validate	O
a	O
variety	O
of	O
identification	O
numbers	O
,	O
such	O
as	O
credit	O
card	O
numbers	O
,	O
IMEI	O
numbers	O
,	O
National	O
Provider	O
Identifier	O
numbers	O
in	O
the	O
United	O
States	O
,	O
Canadian	O
social	O
insurance	O
numbers	O
,	O
Israeli	O
ID	O
numbers	O
,	O
South	O
African	O
ID	O
numbers	O
,	O
Swedish	O
national	O
identification	O
numbers	O
,	O
Swedish	O
Corporate	O
Identity	O
Numbers	O
(	O
OrgNr	O
)	O
,	O
Greek	O
Social	O
Security	O
Numbers	O
( ΑΜΚΑ	O
)	O
,	O
SIM	O
card	O
numbers	O
,	O
European	O
patent	O
application	O
number	O
and	O
survey	O
codes	O
appearing	O
on	O
McDonald	O
's	O
,	O
Taco	O
Bell	O
,	O
and	O
Tractor	O
Supply	O
Co	O
.	O
receipts	O
.	O
</s>
<s>
It	O
is	O
not	O
intended	O
to	O
be	O
a	O
cryptographically	B-Algorithm
secure	I-Algorithm
hash	I-Algorithm
function	I-Algorithm
;	O
it	O
was	O
designed	O
to	O
protect	O
against	O
accidental	O
errors	O
,	O
not	O
malicious	O
attacks	O
.	O
</s>
<s>
The	O
Luhn	B-Algorithm
algorithm	I-Algorithm
will	O
detect	O
all	O
single-digit	O
errors	O
,	O
as	O
well	O
as	O
almost	O
all	O
transpositions	O
of	O
adjacent	O
digits	O
.	O
</s>
<s>
Other	O
,	O
more	O
complex	O
check-digit	O
algorithms	O
(	O
such	O
as	O
the	O
Verhoeff	B-Error_Name
algorithm	I-Error_Name
and	O
the	O
Damm	O
algorithm	O
)	O
can	O
detect	O
more	O
transcription	O
errors	O
.	O
</s>
<s>
The	O
Luhn	B-Algorithm
mod	I-Algorithm
N	I-Algorithm
algorithm	I-Algorithm
is	O
an	O
extension	O
that	O
supports	O
non-numerical	O
strings	O
.	O
</s>
<s>
Therefore	O
,	O
systems	O
that	O
pad	O
to	O
a	O
specific	O
number	O
of	O
digits	O
(	O
by	O
converting	O
1234	O
to	O
0001234	O
for	O
instance	O
)	O
can	O
perform	O
Luhn	B-Algorithm
validation	I-Algorithm
before	O
or	O
after	O
the	O
padding	O
and	O
achieve	O
the	O
same	O
result	O
.	O
</s>
<s>
The	O
algorithm	O
appeared	O
in	O
a	O
United	O
States	O
Patent	O
for	O
a	O
simple	O
,	O
hand-held	O
,	O
mechanical	O
device	O
for	O
computing	O
the	O
checksum	B-Algorithm
.	O
</s>
<s>
The	O
device	O
took	O
the	O
mod	B-Algorithm
10	I-Algorithm
sum	O
by	O
mechanical	O
means	O
.	O
</s>
