Editing ABA routing transit number (section)

===MICR routing number format===
The MICR routing number consists of nine digits:
: XXXXYYYYC
where XXXX is Federal Reserve Routing Symbol, YYYY is ABA Institution Identifier,
and C is the check digit.

====Federal Reserve====
The Federal Reserve uses the ABA RTN system for processing its customers' payments.  The ABA RTNs were originally assigned in the systematic way outlined below, reflecting a financial institution's geographical location and internal handling by the Federal Reserve. Following consolidation of the Federal Reserve's check processing facilities, and the consolidation in the banking industry, the RTN a financial institution uses may not reflect the "Fed District" where the financial institution's place of business is located.  Check processing is now centralized at the Federal Reserve Bank of Atlanta.<ref name="bur05">{{Harv|Burnett|2005}}</ref>

The first two digits of the nine digit RTN must be in the ranges 00 through 12, 21 through 32, 61 through 72, or 80.

The digits are assigned as follows:
* 00 is used by the [[Federal government of the United States|United States Government]]
* 01 through 12 are the "normal" routing numbers, and correspond to the 12 [[Federal Reserve Bank]]s. For example, 0260-0959-3 is the routing number for Bank of America incoming wires in New York, with the initial "02" indicating the [[Federal Reserve Bank of New York]].
* 21 through 32 were assigned only to [[Cooperative banking|thrift institutions]] (e.g. [[credit union]]s and savings banks) through 1985, but are no longer assigned (thrifts are assigned normal 01–12 numbers). Currently they are still used by the thrift institutions, or their successors, and correspond to the normal routing number, plus 20. (For example, 2260-7352-3 is the routing number for Grand Adirondack Federal Credit Union in New York, with the initial "22" corresponding to "02" (New York Fed) plus "20" (thrift).)
* 61 through 72 are special purpose routing numbers designated for use by non-bank payment processors and clearinghouses and are termed Electronic Transaction Identifiers (ETIs), and correspond to the normal routing number, plus 60.
* 80 is used for [[traveler's check]]s

The first two digits correspond to the 12 [[Federal Reserve Bank]]s as follows:

{| class="wikitable"
! Primary<br />(01–12)
! Thrift<br/>(+20)
! Electronic<br/>(+60)
! Federal Reserve Bank
|-
|01 || 21 || 61 || [[Federal Reserve Bank of Boston|Boston]]
|-
|02 || 22 || 62 || [[Federal Reserve Bank of New York|New York]]
|-
|03 || 23 || 63 || [[Federal Reserve Bank of Philadelphia|Philadelphia]]
|-
|04 || 24 || 64 || [[Federal Reserve Bank of Cleveland|Cleveland]]
|-
|05 || 25 || 65 || [[Federal Reserve Bank of Richmond|Richmond]]
|-
|06 || 26 || 66 || [[Federal Reserve Bank of Atlanta|Atlanta]]
|-
|07 || 27 || 67 || [[Federal Reserve Bank of Chicago|Chicago]]
|-
|08 || 28 || 68 || [[Federal Reserve Bank of St. Louis|St. Louis]]
|-
|09 || 29 || 69 || [[Federal Reserve Bank of Minneapolis|Minneapolis]]
|-
|10 || 30 || 70 || [[Federal Reserve Bank of Kansas City|Kansas City]]
|-
|11 || 31 || 71 || [[Federal Reserve Bank of Dallas|Dallas]]
|-
|12 || 32 || 72 || [[Federal Reserve Bank of San Francisco|San Francisco]]
|}

The third digit corresponds to the Federal Reserve check processing center originally assigned to the bank.<ref name="bur05" />

The fourth digit is "0" if the bank is located in the Federal Reserve city proper, and otherwise is 1–9, according to which state in the Federal Reserve district it is.<ref name="bur05" />

====ABA Institution Identifier====
The fifth through eighth digits constitute the bank's unique ABA identity within the given Federal Reserve district.<ref name="bur05" />

====Check digit====
The ninth, [[check digit]] provides a [[checksum]] test using a position-weighted sum of each of the digits. High-speed check-sorting equipment will typically verify the checksum and if it fails, route the item to a reject pocket for manual examination, repair, and re-sorting. Mis-routings to an incorrect bank are thus greatly reduced.

The following condition must hold:<ref name="bo04" />

:{{math|1=(3({{var|d}}{{sub|1}} + {{var|d}}{{sub|4}} + {{var|d}}{{sub|7}}) + 7({{var|d}}{{sub|2}} + {{var|d}}{{sub|5}} + {{var|d}}{{sub|8}}) + ({{var|d}}{{sub|3}} + {{var|d}}{{sub|6}} + {{var|d}}{{sub|9}})) mod 10 = 0}}

: ([[Modulo operation|Mod]] or modulo is the remainder of a division operation.)
In terms of weights, this is 371 371 371. This allows one to catch any single-digit error (incorrectly inputting one digit), together with most transposition errors. 1, 3, and 7 are used because they (together with 9) are [[coprime]] to 10; using a coefficient that is divisible by 2 or 5 would lose information (because <math>5 \cdot 0 = 5 \cdot 2 = 5 \cdot 4 = 5 \cdot 6 = 5 \cdot 8 = 0 \mod 10</math>), and thus would not catch some substitution errors. These do not catch transpositions of two digits that differ by 5 (0 and 5, 1 and 6, 2 and 7, 3 and 8, 4 and 9), but captures other transposition errors.{{citation needed|date=April 2013}}

As an example, consider 111000025 (which is a valid routing number of [[Bank of America]] in [[Virginia]]). Applying the formula, we get:

: {{math|1= (3(1&thinsp;+&thinsp;0&thinsp;+&thinsp;0) + 7(1&thinsp;+&thinsp;0&thinsp;+&thinsp;2) + (1&thinsp;+&thinsp;0&thinsp;+&thinsp;5)) mod 10 = 0}}.

====Routing symbol====
[[File:OCR branch bank identification.svg|50px|right]]

The symbol that delimits a routing transit number is the [[MICR]] [[E-13B]] transit character ⑆ This character, with Unicode value U+2446, appears at right.