Let-a-b-Z-0-lt-a-lt-b-How-would-you-find-the-maximum-largest-prime-gap-in-a-b-Note-Prime-gaps-are-the-distance-between-consecutive-primes-e-g-7-and-11-has-a-prime-gap-4-p-k-P-p-x-p

Question Number 21292 by FilupS last updated on 19/Sep/17

Let a, b \in Z

0 < a < b

How would you find the maximum /

largest prime gap in (a, b) ?

Note :

Prime gaps are the distance between

consecutive primes .

e . g . 7 and 11 has a prime gap 4

p_{k} \in P

∴ \forall p_{x} \forall p_{x + 1} \in (a, b) : p_{x + 1} > p_{x}

p_{x + 1} and p_{x} are consecutive primes

Lets denote δ_{x} = p_{x + 1} - p_{x} as prime gap

for (1, 20), the primes are 2, 3, 5, 7, 11, 13, 17

The prime gaps are :

1, 2, 2, 4, 2, 4

Therefore the largest δ = 4

Is there a more general method ?