OEIS A000101: Record Prime Gaps

We dive into A000101, the OEIS sequence that marks the endpoints of record-breaking prime gaps. Learn what a prime gap is, how the record gaps line up with A002386 on the lower end, and why Ramanujan primes appear as interesting exceptions. We’ll explore the massive computational feats behind gaps that span millions or billions of integers, the contributions of researchers like Tomas Oliveira e Silva and Thomas Nicely, and how these gaps relate to big puzzles like the twin prime conjecture. The entry also provides a formula linking A000101 to related sequences and code in Mathematica and PARI/GP to generate terms, plus graphs and cross-references that deepen our understanding of prime distribution.

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