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The Babylonian cuneiform numerals had a base of 60, inherited from the Sumerian and Akkadian civilizations, and possibly motivated by its large number of divisors. The sexagesimal measurement of time and of geometric angles is a legacy of the Babylonian system. For example, in time, there are 60 seconds in a minute, and 60 minutes in an hour. (a legacy of the Babylonian number system)
The "59-minute rule" is an informal rule in business, whereby (usually near a holiday) employees may be allowed to leave work early, often to beat heavy holiday traffic (the 59 minutes coming from the rule that leaving one full hour early requires the use of leave, whereas leaving 59 minutes early would not).
58 is the sum of the first seven primes
Although fifty-seven is not prime, it is jokingly known as the Grothendieck prime after a legend in which the mathematician Alexander Grothendieck gave it as an example of a prime number, not realizing it was divisible by three and nineteen. The same error was made by another famous mathematician, Hermann Weyl, in a published article.
56 is an Erdős–Woods number, meaning that there is an interval of 57 consecutive integers in which every element has a nontrivial common factor with one of the two endpoints.

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