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).
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 have101, 103, 107, 109
but101-107
is not a 6-gap because there is103
in between and103-109
is not a 6-gap because there is107
in between.- You can see more examples of return in Sample Tests.