Problem Statement

The series of increasing prime numbers begins: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ... The task applies a filter to the series returning groups of successive primes, (s'primes), that differ from the next by a given value or values. Example 1: Specifying that the difference between s'primes be 2 leads to the groups: (Known as Twin primes or Prime pairs) Example 2: Specifying more than one difference between s'primes leads to groups of size one greater than the number of differences. Differences of 2, 4 leads to the groups: In the first group 7 is two more than 5 and 11 is four more than 7; as well as 5, 7, and 11 being successive primes. Differences are checked in the order of the values given, (differences of 4, 2 would give different groups entirely). Note: Generation of a list of primes is a secondary aspect of the task. Use of a built in function, well known library, or importing/use of prime generators from other Rosetta Code tasks is encouraged.

Let's start with the solution:

// Successive primes. Nigel Galloway: May 6th., 2019
let sP n=let sP=pCache|>Seq.takeWhile(fun n->n<1000000)|>Seq.windowed(Array.length n+1)|>Seq.filter(fun g->g=(Array.scan(fun n g->n+g) g.[0] n))
         printfn "sP %A\t-> Min element = %A Max element = %A of %d elements" n (Seq.head sP) (Seq.last sP) (Seq.length sP)
List.iter sP [[|2|];[|1|];[|2;2|];[|2;4|];[|4;2|];[|6;4;2|]]