A dozen is twelve. So why is a baker’s dozen thirteen? It’s from medieval England when a law called “Assize of Bread and Ale” made harsh penalties for bakers who tried to cheat customers. The bakers actually supported it, because they didn’t want to have to compete with bakers who were cheating customers by using less dough to make bread. It did this by standardising the price based on the weight and enforcing harsh punishments for overcharging (which could even include chopping off the baker’s hand). The problem was, it was actually quite common for an honest baker accidentally to not use enough dough. To avoid the punishments, bakers gave their customers one more item than the dozen they asked for, just in case.
Twelve is a good number to pick for this kind of thing, and it’s not surprising it was the standard. Twelve can be divided by 1, 2, 3, 4, 6, and 12 to get another whole number. That means there are many different container and cooking trays that could efficiently store or cook the bread. Twelve actually has more numbers that divide it than any number less than it. In maths, it’s called a “highly composite number“. It’s a shame that they had to go from such a good number, to such an awful number, thirteen. Thirteen is a prime number, which means that it can only divide by itself, and one. If they were cookies, the only rectangular box that could hold all thirteen cookies without any gaps is a single row with all thirteen in that row. Yeah, awful. This is also the reason why we have twelve months, and why today there are groups trying to get us to count in twelves instead of tens.
I thought about which other numbers I could find that are prime and one more than a highly composite number. I called them “Bakery Numbers” and I wrote a really inefficient program to calculate them. The first few popped out quickly, but it took a lot longer to get any more. I got a friend involved who improved the program (a lot). We put it on a fast-ish computer and let it run for one day and one night. From all of that we only got to the 21st Bakery Number, which was 43,243,201.
The code for the BakerBot can be found on Github.