# 1051

This number is a prime.

C. J. Mozzochi utilized 1051 to show that if we let p(*n*)
be the *n*th prime, then there exists a constant *K* such that
p(*n*+1) - p(*n*) is less than *K* p(*n*)^(**1051**/1920). [Post]

1051 = π(1*1051) + π(0*1051) + π(5*1051) + π(1*1051). [Aghasoltan]

The largest known number n such that there is no prime between n^{k} and (n+1)^{k}, where k = 3/2. [Capelle]

The sum of all odd semiprimes less than a hundred. [Silva]

A book known as "The Great Omar" sank with the *Titanic* and has not been recovered. It contained 1051 precious and semi-precious stones set in eighteen-carat gold.

Before the Great Recession of the 1970's, the Dow Jones Industrial Average peaked at 1051 on January 11, 1973. (This is a record that would stand for nearly ten years.) [Cuenta]

There are at least 1051 cases in which the nth Honaker prime has the same number of digits as the nth square. The smallest are 4397 and 1024 (32^2). The largest known are 1066157 and 9998244 (3162^2). Could there possibly be more? [Gaydos]