gap-in-primes

Gap in Primes

The prime numbers are not regularly spaced. For example from 2 to 3 the gap is 1. From 3 to 5 the gap is 2. From 7 to 11 it is 4. Between 2 and 50 we have the following pairs of 2-gaps primes: 3-5, 5-7, 11-13, 17-19, 29-31, 41-43

A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes ( see: http://mathworld.wolfram.com/PrimeGaps.html).

We will write a function gap with parameters:

• g (integer >= 2) which indicates the gap we are looking for

• m (integer > 2) which gives the start of the search (m inclusive)

• n (integer >= m) which gives the end of the search (n inclusive)

In the example above gap(2, 3, 50) will return [3, 5] or (3, 5) or {3, 5} which is the first pair between 3 and 50 with a 2-gap.

So this function should return the first pair of two prime numbers spaced with a gap of g between the limits m, n if these numbers exist otherwise `nil or null or None or Nothing (or ... depending on the language).

In such a case (no pair of prime numbers with a gap of `g`)
In C: return [0, 0]
In C++, Lua, COBOL: return `{0, 0}`. 
In F#: return `[||]`. 
In Kotlin, Dart and Prolog: return `[]`.
In Pascal: return Type TGap (0, 0).

Examples:

• gap(2, 5, 7) --> [5, 7] or (5, 7) or {5, 7}
• gap(2, 5, 5) --> nil. In C++ {0, 0}. In F# [||]. In Kotlin, Dart and Prolog return []`
• gap(4, 130, 200) --> [163, 167] or (163, 167) or {163, 167} ([193, 197] is also such a 4-gap primes between 130 and 200, but it's not the first pair)
• gap(6,100,110) --> nil or {0, 0} or ... : between 100 and 110 we have 101, 103, 107, 109 but 101-107is not a 6-gap because there is 103in between and 103-109is not a 6-gap because there is 107in between.
• You can see more examples of return in Sample Tests.