A prime p is in category 1 if the prime factors of p+1 are 2 and or 3. p is in category 2 if all the prime factors of p+1 are in category 1. p is in category g if all the prime factors of p+1 are in categories 1 to g-1.

The task is first to display the first 200 primes allocated to their category, then assign the first million primes to their category, displaying the smallest prime, the largest prime, and the count of primes allocated to each category.

 
// Erdös-Selfridge categorization of primes. Nigel Galloway: April 12th., 2022
let rec fG n g=match n,g with ((_,1),_)|(_,[])->n |((_,p),h::_) when h>p->n |((p,q),h::_) when q%h=0->fG (p,q/h) g |(_,_::g)->fG n g
let fN g=Seq.unfold(fun(n,g)->let n,g=n|>List.map(fun n->fG n g)|>List.partition(fun(_,n)->n<>1) in let g=g|>List.map fst in if g=[] then None else Some(g,(n,g)))(primes32()|>Seq.take g|>Seq.map(fun n->(n,n+1))|>List.ofSeq,[2;3])
fN 200|>Seq.iteri(fun n g->printfn "Category %d: %A" (n+1) g)
fN 1000000|>Seq.iteri(fun n g->printfn "Category %d: first->%d last->%d count->%d" (n+1) (List.head g) (List.last g) (
 