Have you noticed the number on the publishers page of a book and ever wondered what they mean?  They are printer's code and provides information on the edition and printings of a book.  The print code indicates a print run and does not always guarantee a first edition but certainly provides more information to verify edition.
They may be as simple as a line of numbers or letters:
Example of First Printings:
1 2 3 4 5 6 7 8 9 10

10 9 8 7 6 5 4 3 2 1

ABCD
abcdefg

Once new printings occur the publisher removes a number or letter

For example:

3 4 5 6 7 8 9 10 indicates third printing of the book

Later printings may only use a single number or a very small series.

For example:
 30 31 32   or 30 would all indicate 30th printing of a book.

Some publishers will use a more complicated code.

fFor example
1 2 3 4 5 6   94 95 96 97 97 98

This would indicate first  printing in the year 1994.  To verify first printing you would need to check the copyright date, which would need to be 1994.

There are some publishers that have used unique methods of coding:
D.Appletone&Co.: The print run is at the end of the text (1)
Arcadia House: Not date on the title page, 1 on the verso
Carrick& Evans: Places an A on the verso
Thomas Crowell Co. Inc: 1 on the verso, also a first edtion over a line of letters beginning with B
Random House: First Edition over a numbe line beginning with 2