Prime gap
A prime gap is the difference between two successive prime numbers. The n {\displaystyle n} -th prime gap, denoted g n {\displaystyle g_{n}} or g ( p n ) {\displaystyle g(p_{n})} is the difference between the ( n + 1 ) {\displaystyle (n+1)} th and the n {\displaystyle n} -th prime numbers, i.e., g n = p n + 1 − p n {\displaystyle g_{n}=p_{n+1}-p_{n}} For example, since the first few primes are 2, 3, 5, 7, 11..., we have g 1 = 1 {\displaystyle g_{1}=1} , g 2 = g 3 = 2 {\displaystyle g_{2}=g_{3}=2} , g 4 = 4 {\displaystyle g_{4}=4} .