Prime Gap of 654

Theorem

There exists a prime gap of $654$ between $11\,000\,001\,446\,613\,353$ and $11\,000\,001\,446\,614\,007$.

Proof

$11\,000\,001\,446\,613\,353$ is a prime number.

$11\,000\,001\,446\,614\,007$ is a prime number.

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

$\blacksquare$

Historical Note

This prime gap was reported by David Wells in his Curious and Interesting Numbers of $1986$ as being a record.

However, in $1993$ a prime gap of 864 was found between the smaller prime numbers $6 \, 505 \, 941 \, 701 \, 960 \, 039$ and $6 \, 505 \, 941 \, 701 \, 960 \, 903$, again by Sol Weintraub.

Sources

• 1981: Sol Weintraub: A Large Prime Gap (Math. Comp. Vol. 36: p. 279)  www.jstor.org/stable/2007746

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $11,000,001,446,613,353$