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)
Famous quotes containing the word mathematics:
“I must study politics and war that my sons may have liberty to study mathematics and philosophy.”
—John Adams (1735–1826)
“Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.”
—Walter Reisch (1903–1963)