61 (number) explained
Number: | 61 |
Factorization: | prime |
Prime: | 18th |
Divisor: | 1, 61 |
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,
.
[1] It is also a
centered decagonal number,
[2] and a
centered hexagonal number.
[3] 61 is the fourth cuban prime of the form
where
,
[4] and the fourth
Pillai prime since
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
which ends in the digit 1 in
decimal and whose
reciprocal in base-10 has a
repeating sequence of length
where each digit (0, 1, ..., 9) appears in the repeating sequence the same number of times as does each other digit (namely,
times).
[7] 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.
Sixty-one is the exponent of the ninth Mersenne prime,
M61=261-1=2,305,843,009,213,693,951
[9] and the next candidate exponent for a potential fifth double Mersenne prime:
=22305843009213693951-1 ≈ 1.695 x 10694127911065419641.
[10] 61 is also the largest prime factor in Descartes number,[11]
This number would be the only known odd perfect number if one of its composite factors (22021 = 192 × 61) were prime.[12]
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).
is the last odd-dimensional sphere to contain a unique
smooth structure;
,
and
are the only other such spheres.
[13] [14] In science
Astronomy
In other fields
See also: List of highways numbered 61. 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[15]
- The maximum number of tables that can be joined in a single MariaDB or MySQL query[16]
In sports
References
- R. Crandall and C. Pomerance (2005). Prime Numbers: A Computational Perspective. Springer, NY, 2005, p. 79.
Notes and References
- 2024-02-09 .
- Web site: Sloane's A062786 : Centered 10-gonal numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-30.
- Web site: Sloane's A003215 : Hex (or centered hexagonal) numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-30.
- Web site: Sloane's A002407 : Cuban primes. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-30.
- Web site: Sloane's A063980 : Pillai primes. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-30.
- Web site: Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers). The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-30.
- Dickson, L. E., History of the Theory of Numbers, Volume 1, Chelsea Publishing Co., 1952.
- Web site: Sloane's A005235 : Fortunate numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-30.
- Web site: Sloane's A000043 : Mersenne exponents. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-30.
- Web site: Mersenne Primes: History, Theorems and Lists . . 2023-10-22 .
- Holdener . Judy . Rachfal . Emily . Perfect and Deficient Perfect Numbers . . 126 . 6 . . 2019 . 541–546 . 10.1080/00029890.2019.1584515 . 3956311 . 1477.11012 . 191161070 . .
- 2024-02-27 .
- Wang . Guozhen . Xu . Zhouli . The triviality of the 61-stem in the stable homotopy groups of spheres . . 186 . 2017 . 2 . 501–580 . 10.4007/annals.2017.186.2.3 . 3702672 . 1601.02184 . 119147703 .
- 2023-10-22 .
- Hoyle, Edmund Hoyle's Official Rules of Card Games pub. Gary Allen Pty Ltd, (2004) p. 470
- https://dev.mysql.com/doc/refman/8.0/en/join.html MySQL Reference Manual – JOIN clause