# 73 (number)

__: Natural number__

**Short description**
| ||||
---|---|---|---|---|

Cardinal | seventy-three | |||

Ordinal | 73rd (seventy-third) | |||

Factorization | prime | |||

Prime | 21st | |||

Divisors | 1, 73 | |||

Greek numeral | ΟΓ´ | |||

Roman numeral | LXXIII | |||

Binary | 1001001_{2} | |||

Ternary | 2201_{3} | |||

Quaternary | 1021_{4} | |||

Quinary | 243_{5} | |||

Senary | 201_{6} | |||

Octal | 111_{8} | |||

Duodecimal | 61_{12} | |||

Hexadecimal | 49_{16} | |||

Vigesimal | 3D_{20} | |||

Base 36 | 21_{36} |

**73** (**seventy-three**) is the natural number following 72 and preceding 74. In English, it is the smallest natural number with twelve letters in its spelled out name.

## In mathematics

**73** is the 21st prime number, and emirp with 37, the 12th prime number.^{[1]} It is also the eighth twin prime, with 71. It is the largest minimal primitive root in the first 100,000 primes; in other words, if p is one of the first one hundred thousand primes, then at least one of the numbers 2, 3, 4, 5, 6, ..., **73** is a primitive root modulo p. 73 is also the smallest factor of the first composite generalized Fermat number in decimal: [math]\displaystyle{ 10^{4}+1=10,001=73\times 137 }[/math], and the smallest prime congruent to 1 modulo 24, as well as the only prime repunit in octal (111_{8}). It is the fourth star number.^{[2]}

Notably, 73 is the sole **Sheldon prime** to contain both *mirror* and *product* properties:^{[3]}

- 73, as an emirp, has 37 as its dual permutable prime, a mirroring of its base ten digits, 7 and 3. 73 is the 21st prime number, while 37 is the 12th, which is a second mirroring; and
- 73 has a prime index of 21 = 7 × 3; a product property where the product of its base-10 digits is precisely its index in the sequence of prime numbers.

Arithmetically, from sums of 73 and 37 with their prime indexes, one obtains:

Other properties *ligating* 73 with 37 include:
Template:Bullet list

In binary, 73 is 1001001, while 21 in binary is 10101, and 7 in binary is 111; all which are palindromic. Of the **7** binary digits representing 73, there are **3** ones. In addition to having prime factors 7 and 3, the number 21 represents the ternary (base-3) equivalent of the decimal numeral 7, that is to say: 21_{3} = 7_{10}.

There are 73 three-dimensional arithmetic crystal classes that are part of 230 crystallographic space group types.^{[4]} These 73 groups are specifically **symmorphic** groups such that all operating lattice symmetries have one common fixed isomorphic point, with the remaining 157 groups nonsymmorphic (the 37th prime is 157).

In five-dimensional space, there are 73 Euclidean solutions of 5-polytopes with uniform symmetry, excluding prismatic forms: 19 from the [math]\displaystyle{ \mathrm A_{5} }[/math] simplex group, 23 from the [math]\displaystyle{ \mathrm D_{5} }[/math] demihypercube group, and 31 from the [math]\displaystyle{ \mathrm B_{5} }[/math] hypercubic group, of which 15 equivalent solutions are shared between [math]\displaystyle{ \mathrm D_{5} }[/math] and [math]\displaystyle{ \mathrm B_{5} }[/math] from distinct polytope operations.

In moonshine theory of sporadic groups, 73 is the first *non-supersingular prime* greater than 71. All primes greater than or equal to 73 are non-supersingular, while 37, on the other hand, is the smallest prime number that is not supersingular.^{[5]}

73 is the largest member of the 17-integer matrix definite quadratic that represents all prime numbers: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, **37**, 41, 43, 47, 67, **73**}.^{[6]}

## In science

- The atomic number of tantalum

### In astronomy

- Messier object M73, a magnitude 9.0 apparent open cluster in the constellation Aquarius.
- The New General Catalogue object NGC 73, a barred spiral galaxy in the constellation Cetus.
- The number of seconds it took for the Space Shuttle
*Challenger*OV-099 shuttle to explode after launch. - 73 is the number of rows in the 1,679-bit Arecibo message, sent to space in search for extraterrestrial intelligence.

### In chronology

- The year
**AD 73**, 73 BC, or 1973. - The number of days in 1/5 of a non-leap year.
- The 73rd day of a non-leap year is March 14, also known as Pi Day.

## In other fields

**73** is also:

- The number of books in the Catholic Bible.
^{[7]} - Amateur radio operators and other morse code users commonly use the number 73 as a "92 Code" abbreviation for "best regards", typically when ending a QSO (a conversation with another operator). These codes also facilitate communication between operators who may not be native English speakers.
^{[8]}In Morse code, 73 is an easily recognized palindrome: ( - - · · · · · · - - ). *73*(also known as*73 Amateur Radio Today*) was an amateur radio magazine published from 1960 to 2003.- 73 was the number on the Torpedo Patrol (PT) boat in the TV show
*McHale's Navy*. - The registry of the U.S. Navy's nuclear aircraft carrier USS
*George Washington*(CVN-73), named after U.S. President George Washington. *No. 73*was the name of a 1980s children's television programme in the United Kingdom. It ran from 1982 to 1988 and starred Sandi Toksvig.- Pizza 73 is a Canadian pizza chain.
- Game show
*Match Game '73*in 1973. - Fender Rhodes Stage 73 Piano.
- Sonnet 73 by William Shakespeare.
- The number of the French department Savoie.
- On a CB radio, 10-73 means "speed trap at..."

## In sports

- In international curling competitions, each side is given 73 minutes to complete all of its throws.
- In baseball, the single-season home run record set by Barry Bonds in 2001.
- In basketball, the number of games the Golden State Warriors won in the 2015–16 season (73-9), the most wins in NBA history.
- NFL: In the 1940 NFL championship game, the Bears beat the Redskins 73–0, the largest score ever in an NFL game. (The Redskins won their previous regular season game, 7–3.)

## Popular culture

*The Big Bang Theory*

73 is Sheldon Cooper's favorite number in The Big Bang Theory. He first expresses his love for it in "The Alien Parasite Hypothesis".^{[9]} Jim Parsons was born in the year 1973.^{[10]} "The Alien Parasite Hypothesis" is the 73rd episode of The Big Bang Theory. He often wears a t-shirt with the number 73 on it.^{[11]}

## See also

- List of highways numbered 73

## References

- ↑ "Sloane's A006567 : Emirps". OEIS Foundation. https://oeis.org/A006567.
- ↑
^{2.0}^{2.1}"Sloane's A003154 : Centered 12-gonal numbers. Also star numbers: 6*n*(n-1) + 1". OEIS Foundation. https://oeis.org/A003154. - ↑ Pomerance, Carl; Spicer, Chris (February 2019). "Proof of the Sheldon conjecture".
*American Mathematical Monthly***126**(8): 688–698. doi:10.1080/00029890.2019.1626672. https://math.dartmouth.edu/~carlp/sheldon02132019.pdf. - ↑ Sloane, N. J. A., ed. "Sequence A004027 (Number of arithmetic n-dimensional crystal classes.)". OEIS Foundation. https://oeis.org/A004027. Retrieved 2022-11-29.
- ↑ Sloane, N. J. A., ed. "Sequence A002267 (The 15 supersingular primes)". OEIS Foundation. https://oeis.org/A002267. Retrieved 2022-10-13.
- ↑ Sloane, N. J. A., ed. "Sequence A154363 (Numbers from Bhargava's prime-universality criterion theorem)". OEIS Foundation. https://oeis.org/A154363.
- ↑ "Catholic Bible 101". http://www.catholicbible101.com/thebible73or66books.htm.
- ↑ "Ham Radio History". http://www.arrl.org/ham-radio-history.
- ↑ "The Big Bang Theory (TV Series) - The Alien Parasite Hypothesis (2010) - Jim Parsons: Sheldon Cooper". https://www.imdb.com/title/tt1632225/characters/nm1433588.
- ↑ "Jim Parsons". https://www.imdb.com/name/nm1433588/.
- ↑ "The Alien Parasite Hypothesis".
*The Big Bang Theory*. Season 4. Episode 10.

Original source: https://en.wikipedia.org/wiki/73 (number).
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