61 (number)

61 (sixty-one) is the natural number following 60 and preceding 62.

In mathematics
61 is the 18th prime number, and a twin prime with 59. As a centered square number, it is the sum of two consecutive squares, $$5^2 + 6^2$$. It is also a centered decagonal number, and a centered hexagonal number.

61 is the fourth cuban prime of the form $$p = \frac {x^{3} - y^{3}}{x - y}$$ where $$x = y + 1$$, and the fourth Pillai prime since $$8! + 1$$ is divisible by 61, but 61 is not one more than a multiple of 8. It is also a Keith number, as it recurs in a Fibonacci-like sequence started from its base 10 digits: 6, 1, 7, 8, 15, 23, 38, 61, ...

61 is a unique prime in base 14, since no other prime has a 6-digit period in base 14, and palindromic in bases 6 (1416) and 60 (1160). It is the sixth up/down or Euler zigzag number.

61 is the smallest proper prime, a prime $$p$$ which ends in the digit 1 in decimal and whose reciprocal in base-10 has a repeating sequence of length $$p - 1,$$ where each digit (0, 1, ..., 9) appears in the repeating sequence the same number of times as does each other digit (namely, $$\tfrac {p-1}{10}$$ times).

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).

There are sixty-one 3-uniform tilings, where on the other hand, there are one hundred and fifty-one 4-uniform tilings (with 61 the eighteenth prime number, and 151 the thirty-sixth, twice the index value).

Sixty-one is the exponent of the ninth Mersenne prime, $$M_{61} = 2^{61} - 1 = 2,305,843,009,213,693,951$$ and the next candidate exponent for a potential fifth double Mersenne prime: $$M_{M_{61}} = 2^{2305843009213693951} - 1 \approx 1.695 \times 10^{694127911065419641}.$$

61 is also the largest prime factor in Descartes number,

$$3^2 \times 7^2 \times 11^2 \times 13^2 \times 19^2 \times 61 = 198585576189.$$

This number would be the only known odd perfect number if one of its composite factors (22021 = 192 × 61) were prime.

61 is the largest prime number (less than the largest supersingular prime, 71) that does not divide the order of any sporadic group (including any of the pariahs).

The exotic sphere $$S^{61}$$ is the last odd-dimensional sphere to contain a unique smooth structure; $$S^{1}$$, $$S^{3}$$ and $$S^{5}$$ are the only other such spheres.

In science

 * The chemical element with the atomic number 61 is promethium.

Astronomy

 * Messier object M61, a magnitude 10.5 galaxy in the constellation Virgo
 * The New General Catalogue object NGC 61, a double spiral galaxy in the constellation Cetus
 * 61 Ursae Majoris is located about 31.1 light-years from the Sun.
 * 61 Cygni was christened the "Flying Star" in 1792 by Giuseppe Piazzi (1746–1826) for its unusually large proper motion.

In other fields
Sixty-one is:
 * The number of the French department Orne
 * The code for international direct dial phone calls to Australia
 * 61*, a 2001 baseball movie directed by Billy Crystal
 * Highway 61 Revisited is a Bob Dylan album
 * The Highway 61 Blues Festival occurs annually in Leland, Mississippi
 * Highway 61 is a 1991 film set on U.S. Route 61
 * U.S. Route 61 is the highway that inspired so much attention on "Highway 61"
 * Part 61 is a law created by the FAA regarding medical exams. This law has often come under attack by AOPA.
 * The P-61 is the Northrop-designed fighter first designated as the XP-61. It first flew on May 26, 1942. It is also known as the Black Widow as it was the first fighter aircraft designed to be a night fighter
 * Sixty 1 is a brand tobacco produced by Nationwide Tobacco
 * 61A is the London address of Margot Wendice (Grace Kelly) and Tony Wendice (Ray Milland) in the movie Dial M for Murder
 * 1 Liberty Place is one of Philadelphia's tallest buildings at 61 stories
 * The number of cadets on The Summerall Guards
 * The number of points required to win a "standard" game of cribbage
 * The maximum number of tables that can be joined in a single MariaDB or MySQL query

In sports

 * New York Yankees right fielder Roger Maris hit 61 home runs in 1961, breaking Babe Ruth's single-season record until it was surpassed in 1998 by Mark McGwire and Sammy Sosa. The American League record was broken 61 years later in 2022, by Aaron Judge.
 * Nolan Ryan and Tom Seaver each had 61 career shutouts
 * Hockey great Wayne Gretzky holds or shares 61 NHL records (40 for regular season, 15 for Stanley Cup playoff, and 6 for All-Star Games)
 * Rotation, a variation of pool, is sometimes called 61
 * Richie Evans' NASCAR Whelen Modified Tour car number was 61 until his death in 1985
 * The number of the laps of the first Formula One night race, Singapore Grand Prix.