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73 - The best number

73 - What a fascinating number!

73, Heinz

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What an amazingly amusing paper. Thanks, Heinz…

Most numbers are equally special in different ways :).

For example:

Seventy-two is the sum of four consecutive primes (13 + 17 + 19 + 23), as well as the sum of six consecutive primes (5 + 7 + 11 + 13 + 17 + 19). The product of 8 and 9, 72 is a pronic number.

The sum of Euler’s totient function φ( x ) over the first fifteen integers is 72. There are 17 solutions to the equation φ( x ) = 72, more than any integer below 72, making it a highly totient number.

72 is the smallest number whose fifth power is the sum of five smaller fifth powers: 195 + 435 + 465 + 475 + 675 = 725.

The sum of the eighth row of Lozanić’s triangle is 72.

In a plane, the exterior angles of a regular pentagon measure 72 degrees each.

In base 10, the number 72 is a Harshad number.

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QRPers have known this for years :slight_smile:

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