Twin concatenations

Éric Angelini came up with this idea of listing products (one per line) where the multipliers introducing the line are the positive integers and the smallest possible multiplicands (after the initial line) are deduced from the products, given that the concatenations of the products (to the right of the equal signs) must be the same as the concatenations of the multipliers and multiplicands (in order, to the left of the equal signs), from the beginning, as far as it will go.

On the MathFun mail list, Éric shared Gilles Esposito-Farese's version that makes the multipliers the nonnegative integers (up to 50), instead of the positive-integers versions shown on Éric's blog:

 0 * 0 = 0
 1 * 0 = 0
 2 * 5 = 10
 4 * 63659 = 254636
 5 * 119 = 595
...

For some reason Gilles skipped 3. Which makes his output for lines 4 to 50 incorrect. Ouch!

Here is my correction:

 0 * 0 = 0
 1 * 0 = 0
 2 * 5 = 10
 3 * 846 = 2538
 4 * 1 = 4
 5 * 1283 = 6415
 6 * 2 = 12
 7 * 1194673 = 8362711
 8 * 118342264792783 = 946738118342264
 9 * 88 = 792
10 * 7839881 = 78398810
11 * 7127164651933786 = 78398811171271646
12 * 432781551 = 5193378612
13 * 332908885487176222196 = 4327815511333290888548
14 * 512587299724651848 = 7176222196145125872
15 * 664831 = 9972465
16 * 11550979 = 184815664
...

Here is my listing up to 1000. Please let me know if you see an error!