# ARCHSIX

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interesting information [adapted from Wikipedia]:

An arch is a structure that spans a space  while  supporting weight.

Arches appeared as early as the 2nd millennium BC in Mesopotamian brick architecture,
their systematic use started with the Ancient Romans who were the first to apply the technique to a wide range of structures.

Six is the first perfect number

Six is the second smallest composite number, its proper divisors being 1, 2 and 3.

Since six equals the sum of these proper divisors, six is the smallest perfect number, Granville number, and $\mathcal{S}$-perfect number.

As a perfect number, 6 is related to the Mersenne prime 3, since 21(22 - 1) = 6.

(The next perfect number is 28.) It is the only even perfect number that is not the sum of successive odd cubes.

Being perfect six is the root of the 6-aliquot tree, and is itself the aliquot sum of only one number;

the square number, 25. Unrelated to 6 being a perfect number, a Golomb ruler of length 6 is a "perfect ruler."

Six is a congruent number.

Six is the first discrete biprime (2.3) and the first member of the (2.q) discrete biprime family.

Six is the only number that is both the sum and the product of three consecutive positive numbers.

Six is a harmonic divisor number and a highly composite number. The next highly composite number is 12.

The smallest non-abelian group is the symmetric group S3 which has 3! = 6 elements.

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