Prime Curios!: 60

60
(another Prime Pages' Curiosity)

Curios:

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The largest integer such that all smaller integers relatively prime to it are either a prime, a power of a prime, or 1. [Noe]

The smallest number which is the sum of two odd primes in six different ways. [Wolman]

The smallest composite number which is the order of a simple group, namely A5 (the alternating group on 5 letters). [Terr]

If the first 1000 primes are placed (left-to-right) in ten columns, the number 60 can be added to 60 prime numbers with the resultant prime sum in the column below the original prime. E.g., the 30th prime number is 113, if you add 60, you get 173, the 40th prime number; the 230th prime is 1451 and the 240th prime is 1511 -- a difference of sixty! [Busch]

The largest known positive integer that cannot be written as p * q + r, where p, q, r are three distinct primes. [Capelle]

(There is one curio for this number that has not yet been approved by an editor.)

To link to this page use http://primes.utm.edu/curios/page.php?number_id=393