High Quality Content by WIKIPEDIA articles! A prime gap is the difference between two successive prime numbers. The n-th prime gap, denoted gn, is the difference between the (n + 1)-th and the n-th prime number, i.e. gn = pn + 1 ? pn. In reality, prime gaps of P numbers can occur at numbers much smaller than P#. For instance, the smallest sequence of 71 consecutive composite numbers occurs between 31398 and 31468, whereas 71# has twenty-seven digits - its full decimal expansion being 557940830126698960967415390. Although the average gap between primes increases as the natural logarithm of the integer, the ratio of the maximum prime gap to the integers involved also increases as larger and larger numbers and gaps are encountered.

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