Hamming cube of primes: cp4space.hatsya.com/2021/07/20

Make an infinite graph whose vertices are the binary representations of prime numbers and whose edges represent flipping a single bit of this representation. (For instance, 2 and 3 are neighbors.) Surprisingly, it is not connected! 2131099 has no neighbors.

See also the same question on MathOverflow, a year ago: mathoverflow.net/q/363083/440

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@11011110 I've asked the same question a couple of years ago because it is related to the certificate complexity of being a prime. It got the answer 47867742232066880047611079, see
mathoverflow.net/questions/316

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