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

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, ${\displaystyle 5^{2}+6^{2}}$.^[1] It is also a centered decagonal number,^[2] and a centered hexagonal number.^[3]

61 is the fourth cuban prime of the form ${\displaystyle p={\frac {x^{3}-y^{3}}{x-y}}}$ where ${\displaystyle x=y+1}$,^[4] and the forth Pillai prime since ${\displaystyle 8!+1}$ is divisible by 61, but 61 is not one more than a multiple of 8.^[5] 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, ...^[6]

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 ${\displaystyle p}$ which ends in the digit 1 in decimal and whose reciprocal in base-10 has a repeating sequence of length ${\displaystyle p-1,}$ where each digit (0, 1, ..., 9) appears in the repeating sequence the same number of times as does each other digit (namely, ${\displaystyle {\tfrac {p-1}{10}}}$ times).^[7]: 166

In the list of Fortunate numbers, 61 occurs thrice, since adding 61 to either the tenth, twelfth or seventeenth primorial gives a prime number^[8] (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^[9] (with 61 the eighteenth prime number, and 151 the thirty-sixth, twice the index value).^{[10][lower-alpha 1]}

Sixty-one is the exponent of the ninth Mersenne prime, ${\displaystyle M_{61}=2^{61}-1=2,305,843,009,213,693,951}$^[15] and the next candidate exponent for a potential fifth double Mersenne prime: ${\displaystyle M_{M_{61}}=2^{2305843009213693951}-1\approx 1.695\times 10^{694127911065419641}.}$^[16]

61 is also the largest prime factor in Descartes number,^[17]

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

This number would be the only known odd perfect number if one of its composite factors (22021 = 19² × 61) were prime.^[18]

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

The exotic sphere ${\displaystyle S^{61}}$ is the last odd-dimensional sphere to contain a unique smooth structure; ${\displaystyle S^{1}}$, ${\displaystyle S^{3}}$ and ${\displaystyle S^{5}}$ are the only other such spheres.^[19][20]

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

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^[21]
• The maximum number of tables that can be joined in a single MariaDB or MySQL query^[22]

• 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.