In Mathematics
It is the 18th prime number. The previous is 59, with which it comprises a twin prime. Sixty-one is a cuban prime of the form .
Sixty-one might be the largest prime that divides the product of the next two primes plus 1. If there is a larger such prime, it would have to be greater than 179,424,673.
61 is 9th Mersenne prime exponent. (261 − 1 = 2,305,843,009,213,693,951)
Sixty-one is the sum of two squares, 52 + 62, and it is also a centered square number, a centered hexagonal number and a centered decagonal number.
Since 8! + 1 is divisible by 61 but 61 is not one more than a multiple of 8, 61 is a Pillai prime. In the list of Fortunate numbers, 61 occurs thrice, since adding 61 to either the tenth, twelfth or seventeenth primorial gives a prime number (namely 6,469,693,291; 7,420,738,134,871; and 1,922,760,350,154,212,639,131).
It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 6, 1, 7, 8, 15, 23, 38, 61...
Read more about this topic: 61 (number)
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