Marshall Lochbaum
Have functionality you want to see as a BQN library? Request it here! I'll be directing BQN programmers in search of things to do towards this page.
For best results, include links to resources describing the functionality and other implementations, especially in array languages. Good resources in general are [dfns](https://dfns.dyalog.com/n_contents.htm), [J essays](https://code.jsoftware.com/wiki/Essays), Rosetta Code ([APL](https://rosettacode.org/wiki/Category:APL), [J](https://rosettacode.org/wiki/Category:J)), and Julia codebases such as [JuliaMath](https://github.com/JuliaMath).
Star the projects you would use, and edit the request to indicate current status if you've published anything relevant. The chat thread here might also be useful to coordinate efforts.

Top Answer

Marshall Lochbaum
#### JSON
One of the more common formats for data these days, so it would be nice to have a solid library with good validation for reading and writing. There are multiple possibilities for how to format objects on the BQN side.
[Basic decoder](https://codeberg.org/CptJimKirk/bqn-rest/src/branch/master/JSON.bqn) in bqn-rest.

Answer #2

Marshall Lochbaum
#### Polynomial utilities
Add, multiply, evaluate, and solve definitely. Should it have a way to represent complex polynomials in a real-only BQN? It needs to be able to handle complex roots.
Some simple utilities [on bqncrate](https://mlochbaum.github.io/bqncrate/?q=polynomial). Julia has a solver [here](https://github.com/JuliaMath/Polynomials.jl/blob/master/src/polynomials/multroot.jl). See also [Wikipedia](https://en.wikipedia.org/wiki/Root-finding_of_polynomials#Roots_of_polynomials).

Answer #3

Marshall Lochbaum
#### Prime number utilities
Primality sieving, testing, Pi function, factorization, etc.
Resources: Julia's [Primes.js](https://github.com/JuliaMath/Primes.jl/blob/master/src/Primes.jl); [RosettaCode](https://rosettacode.org/wiki/Category:Prime_Numbers).
Marshall has implemented fairly good versions of these [in bqn-libs](https://github.com/mlochbaum/bqn-libs/blob/master/primes.bqn). Limited to `2⋆53` because it uses native numbers.