Generally on the face of a check there is some numbers such as 66-156 over a line and under it 531

I think it has to do with the Federal Reserve District, routing number, etc.

What do these numbers mean and are they required to be on ALL checks including official checks?

The beginning of Appendix A to Regulation CC still explains routing & transit numbers, although the information is now less relevant to that regulation. Their presence in the MICR line is what allows checks to be routed through the clearing system unseen by human eyes.

I'm not talking about the micr line. I'm talking about a number that usually appears at the top of the check, close to the account number. Usually in the upper right hand corner of the check.

From Appendix A:

A paying bank generally is identified on the face of a check by its routing number in both the fractional form (which generally appears in the upper right–hand corner of the check...

I found it. Thanks
Fractional Form

The fractional form of the routing number is shown most commonly as a multi-digit fraction with a hyphenated numerator and a three or four-digit denominator. Each part is labeled in the number below.

City Prefix 1 2 - 3 4 5 ABA Institution Identifier


6 7 8
Federal Reserve routing Symbol

The geographical base for the ABA's original numbering system was the network of reserve cities in existence at that time. The city prefix served to identify the source of the document by city (or by state). numbers 1 through 49 belonged to reserve cities and major banking centers, who were assigned the numbers in order of their populations.

numbers 50 through 99 designated the states and were assigned in east-to-west order. The numbers 50, 60, 70, 80 and 90 were given to states containing the principal collecting centers - New York, Pennsylvania, Illinois, Missouri and California, respectively. Succeeding numbers in each group were assigned to the states surrounding these collecting centers; exceptions were Hawaii and Alaska, whose prefixes were assigned long after those of the older states. Prefix number 101 was designated for use by territories and dependencies. The complete list of city and state prefix numbers appears following this explanatory section.

The fractional form of the routing number, like the MICR, also includes the Federal Reserve routing symbol and the institution identifier but with these differences:

1. The institution identifier appears as part of the hyphenated numerator and significant zeroes are dropped (a one digit institution identifier would be printed without three zeroes preceding it).

2. The Federal Reserve routing symbol appears as the three or four digit denominator and in districts 1 through 9, the zero is dropped from the first position of the symbol