steps-in-primes

Steps in Primes

The prime numbers are not regularly spaced. For example from 2 to 3 the step is 1. From 3 to 5 the step is 2. From 7 to 11 it is 4. Between 2 and 50 we have the following pairs of 2-steps primes:

3, 5 - 5, 7, - 11, 13, - 17, 19, - 29, 31, - 41, 43

We will write a function step with parameters:

• g (integer >= 2) which indicates the step 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 step(2, 2, 50) will return [3, 5] which is the first pair between 2 and 50 with a 2-steps.

So this function should return the first pair of the two prime numbers spaced with a step of g between the limits m, n if these g-steps prime numbers exist otherwise nil or null or None or Nothing or [] or "0, 0" or {0, 0} or 0 0(depending on the language).

Examples:

step(2, 5, 7) --> [5, 7] or (5, 7) or {5, 7} or "5 7"

step(2, 5, 5) --> nil or ... or [] in Ocaml or {0, 0} in C++

step(4, 130, 200) --> [163, 167] or (163, 167) or {163, 167}

• See more examples for your language in "RUN"

• Remarks:

([193, 197] is also such a 2-steps primes between 130 and 200 but it's not the first pair).

step(6, 100, 110) --> [101, 107] though there is a prime between 101 and 107 which is 103; the pair 101-103 is a 2-step.

Notes:

The idea of "step" is close to that of "gap" but it is not exactly the same. For those interested they can have a look at https://mathworld.wolfram.com/PrimeGaps.html.

A "gap" is more restrictive: there must be no primes in between (101-107 is a "step" but not a "gap". Next kata will be about "gaps":-).

For Go: nil slice is expected when there are no step between m and n. Example: step(2,4900,4919) --> nil