61
This number is a prime.
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The smallest prime that can be written as the sum of a prime number of primes to prime powers in a prime number of ways: 22 + 23 + 72, 22 + 52 + 25, and 32 + 52 + 33. [Hartley]
The smallest prime for which the decimal expansion of the reciprocal 1/61 contains all 10 digits in equal proportions. [Hartley]
The largest known prime of the form Ack(m, m), where Ack is the Ackermann function (which grows faster than an exponential function). Ack(3, 3) = 61. [Hartley]
There are 61 abstract groups of order 1464. Note that 61 divides 1464. [Hartley]
Cyclist Lance Armstrong defeated Jan Ullrich by 61 seconds in the 2003 Tour de France. [Hartley]