Rules: As in a regular crossword, except that digits are filled in rather than letters and the clues refer to the numbers thus formed. Numbers read from left to right and from top to bottom in the decimal number system except where otherwise noted, and do not start with a zero. Normally, all multidigit numbers will be clued and all single-digit numbers won’t.
Across: 1. A divisor of 2 across. 2. A multiple of 1 down.
Down: 1. Different from 1 across.
The earliest crossnumber that I know of is puzzle 239 in H. E. Dudeney’s 536 Puzzles (Curiously, the Bulgarian translation of this book is titled 525 Glavoblyskanitsi, and the Russian one is 520 Golovolomok). It is of size 11 by 11 and uses black squares as separators rather than walls.