Vandon

Lifetime ARP: 14,493

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78 forms a Ruth–Aaron pair with 77. A Ruth–Aaron pair consists of two consecutive integers (e.g., 714 and 715) for which the sums of the prime factors of each integer are equal:
714 = 2 × 3 × 7 × 17
and
715 = 5 × 11 × 13
-and-
2 + 3 + 7 + 17 = 5 + 11 + 13 = 29.

During World War II in Sweden at the border with Norway, "77" was used as a shibboleth (password), because the tricky pronunciation in Swedish made it easy to instantly discern whether the speaker was native Swedish, Norwegian, or German.

There are 76 unique compact uniform hyperbolic honeycombs in the third dimension that are generated from Wythoff constructions. In hyperbolic geometry, a uniform honeycomb in hyperbolic space is a uniform tessellation of uniform polyhedral cells. In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.

75 is a self number because there is no integer that added up to its own digits adds up to 75. A self number in a given number base b is a natural number that cannot be written as the sum of any other natural number n and the individual digits of n. 20 is a self number (in base 10), because no such combination can be found (all n < 15 give a result less than 20; all other n give a result greater than 20). 21 is not, because it can be written as 15 + 1 + 5 using n = 15.

74 is a sad number. In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2 + 3^2 = 10, and 1^2 + 0^2 = 1. On the other hand, 4 is sad number because the sequence starting with 4^2 = 16 and 1^2 + 6^2 = 37 eventually reaches 2^2 + 0^2 = 4, the number that started the sequence, and so the process continues in an infinite cycle without ever reaching 1.

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