# 11

This number is a prime.

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The largest prime number that cannot be written as the sum of four hexagonal numbers. Note that it is the only prime number that cannot be represented using five hexagonal numbers. [Capelle]

The largest integer that cannot be expressed as a sum of (two or more) distinct primes. [Capelle]

The smallest tetradic prime. [Capelle]

There is no known number with multiplicative persistence > 11. [Capelle]

The smallest number of a finite set of numbers inscribed on the faces of a Mughal gold box in the shape of an icosahedron: 11, 20, 21, 31, 41, 51, 61, 71, 81, 91, 101, 201, 202, 301, 401, 501, 601, 701, 801, and 901. An accompanying manuscript note records that the box was found in Tipu Sultan's treasury, after the fall of Seringapatam (India) in 1799. Some research has been devoted to the interpretation of the 20 Arabic numerals of this box, which at first appeared to be unrelated. Among the 11 composite numbers of this list, what's the smallest? [Capelle]