Prime Gaps

A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes. See this Resource for more information.

The prime numbers are not regularly spaced. For example gap between:

• 2 and 3 is 1
• 3 and 5 is 2
• 7 and 11 is 4

Create a function with following parameters:

g (integer >= 2)
# Gap between the consecutive primes

a (integer > 2)
# Start of the search (a inclusive)

b (integer >= a)
# End of the search (b inclusive)

... and returns the first pair of two prime numbers spaced with a gap of g between the limits a and b.

prime_gaps(2, 3, 50) ➞ [3, 5]

# 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.

# [3, 5] is the first pair between 3 and 50 with a 2-gap.

Examples

prime_gaps(2, 5, 7) ➞ [5, 7]

prime_gaps(2, 5, 5) ➞ None

prime_gaps(4, 130, 200) ➞ [163, 167]

Notes

Return None if consecutive prime numbers are not found with the required gap.