Prime gap

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A prime gap is the difference between two successive prime numbers. The n-th prime gap, denoted gn or g(pn) is the difference between the (n+1)th and the n-th prime numbers, i.e., gn=pn+1−pn For example, since the first few primes are 2, 3, 5, 7, 11..., we have g1=1, g2=g3=2, g4=4. The sequence gn of prime gaps has been extensively studied; however, many questions and conjectures remain unanswered. The first 60 prime gaps are: 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, 4, 6, 2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 10, 6, 6, 6, 2, 6, 4, 2, ... (sequence A001223 in the OEIS). By the definition of gn every prime can be written as pn+1=2+∑i=1ngi.

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