OEIS A000230: Smallest Primes for Prime Gaps

We unpack OEIS A000230—the first prime that starts a prime gap of a given size. The episode traces how this sequence marks the very beginnings of new gaps as we move along the primes, notes why small gaps appear early while larger gaps lie further ahead, and connects this edge behavior to the prime number theorem. We also discuss open questions about which gaps occur and how often they appear as numbers grow.

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