First Occurrence of Prime Gap of 864

Theorem

The first occurrence of a prime gap of $864$ is between $6 \, 505 \, 941 \, 701 \, 960 \, 039$ and $6 \, 505 \, 941 \, 701 \, 960 \, 903$.


Proof

$6 \, 505 \, 941 \, 701 \, 960 \, 039$ is a prime number.

$6 \, 505 \, 941 \, 701 \, 960 \, 903$ is a prime number.

It can be checked that all numbers between these two are composite.

It can also be checked by computer that there is no prime gap of $864$ between smaller prime numbers.

$\blacksquare$


Sources

  • 1993: Sol Weintraub: A Prime Gap of $864$ (J. Recr. Math. Vol. 25: pp. 42 – 43)
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $6,505,941,701,960,039$
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