The title reminds me of the occasion when my academic grandfather lectured to the London Mathematical Society on “Moore graphs”. Unfortunately, someone got it wrong, and his lecture was billed as “More graphs”.
But here I really do mean what I wrote.
The function gnu(n) (for Group NUmber) is the number of groups of order n (up to isomorphism). It is an extremely irregular function. It is known up to 2047, and of all the groups of these orders, more than 99% have order 1024. The number is about 5×1010, which is itself dwarfed by the number of groups of the next order 2048, which is about 1.77×1015. However, it is an important function, and precise values are very much needed, as well as providing a computational challenge to existing algorithms and computing facilities. See this article for comments and elaborations.
Now Alexander Konovalov has set up a crowdsourcing project, the “Gnu Project“, to calculate further values of the function, filling in some gaps in the presently known values. He has made available a GAP package to enable anyone to contribute. (The GAP website is here, in case you need to download this free computational system for algebra and discrete mathematics.) According to Alexander, a forthcoming release of GAP will be optimized so as to steamroll over problems of this type.
Instructions for getting and using the package and contributing to the database are provided. Take a look, and lend a hand!