61 (number)

For the Cyrillic letter, seeЫ.

← 60 61 62 →
←60616263646566676869→ List of numbers Integers ←0102030405060708090→
Cardinal	sixty-one
Ordinal	61st (sixty-first)
Factorization	prime
Prime	18th
Divisors	1, 61
Greek numeral	ΞΑ´
Roman numeral	LXI
Binary	1111012
Ternary	20213
Senary	1416
Octal	758
Duodecimal	5112
Hexadecimal	3D16

61(sixty-one) is thenatural numberfollowing60and preceding62.

In mathematics

61is the 18thprime number,and atwin primewith59.As acentered square number,it is the sum of two consecutivesquares,$5^{2}+6^{2}$.It is also acentered decagonal number,and acentered hexagonal number.

61 is the fourthcuban primeof the form$p={\frac {x^{3}-y^{3}}{x-y}}$where$x=y+1$,and the fourthPillai primesince$8!+1$is divisible by 61, but 61 is not one more than a multiple of 8.It is also aKeith 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 aunique primeinbase 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 orEuler zigzagnumber.

61 is the smallestproper prime,a prime$p$which ends in the digit 1 indecimaland whosereciprocalin base-10 has arepeating sequenceof 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 ofFortunate numbers,61 occurs thrice, since adding 61 to either the tenth, twelfth or seventeenthprimorialgives 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-one3-uniform tilings,where on the other hand, there are one hundred and fifty-one4-uniform tilings(with 61 the eighteenthprime number,and151the thirty-sixth, twice theindexvalue).

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

61 is also the largestprime factorinDescartes 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 oddperfect numberif one of its composite factors (22021 = 19²× 61) were prime.

61 is the largestprime number(less than the largestsupersingular prime,71) that does not divide the order of anysporadic group(including any of thepariahs).

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

In science

• The chemical element with theatomic number61 ispromethium.

Astronomy

• Messier objectM61,amagnitude10.5galaxyin theconstellationVirgo
• TheNew General CatalogueobjectNGC 61,a doublespiral galaxyin the constellationCetus
• 61 Ursae Majorisis located about 31.1 light-years from the Sun.[1]
• 61 Cygniwas christened the "Flying Star" in 1792 by Giuseppe Piazzi (1746–1826) for its unusually large proper motion.[2]

In other fields

See also:List of highways numbered 61

Sixty-oneis:

• The number of the French departmentOrne
• Thecode for international direct dialphonecalls toAustralia
• 61*,a 2001baseball moviedirected byBilly Crystal
• Highway 61 Revisitedis aBob Dylanalbum
• The Highway 61 Blues Festival occurs annually in Leland,Mississippi
• Highway 61is a 1991 film set on U.S. Route 61
• U.S. Route 61is the highway that inspired so much attention on "Highway 61"
• Part 61 is a law created by theFAAregarding medical exams. This law has often come under attack byAOPA.
• TheP-61is the Northrop-designed fighter first designated as the XP-61. It first flew on May 26, 1942. It is also known as theBlack Widowas it was the first fighter aircraft designed to be a night fighter
• Sixty 1 is a brand tobacco produced by Nationwide Tobacco
• 61A is theLondonaddress ofMargot Wendice(Grace Kelly) andTony Wendice(Ray Milland) in the movieDial M for Murder
• 1 Liberty Place is one ofPhiladelphia's tallest buildings at 61 stories
• The number of cadets onThe Summerall Guards
• The number of points required to win a "standard" game ofcribbage
• The maximum number of tables that can be joined in a singleMariaDBorMySQLquery

In sports

• New York Yankeesright fielderRoger Marishit 61 home runs in 1961, breaking Babe Ruth's single-season record until it was surpassed in 1998 byMark McGwireandSammy Sosa.The American League record was broken 61 years later in 2022, byAaron Judge.
• Nolan RyanandTom Seavereach had 61 career shutouts
• Hockey greatWayne Gretzkyholds or shares 61NHLrecords (40 for regular season, 15 for Stanley Cup playoff, and 6 for All-Star Games)
• Rotation,a variation ofpool,is sometimes called 61
• Richie Evans'NASCAR Whelen Modified Tourcar number was 61 until his death in 1985
• The number of the laps of the firstFormula Onenight race,Singapore Grand Prix.

References

• R. Crandall and C. Pomerance (2005).Prime Numbers: A Computational Perspective.Springer, NY, 2005, p. 79.