73 Is A Prime Number

Natural number

← 72 73 74 →
← 70 71 72 73 74 75 76 77 78 79 → Listing of numbers Integers ← 0 x 20 30 forty 50 sixty 70 80 xc →
Primal	lxx-three
Ordinal	73rd (70-third)
Factorization	prime
Prime number	21st
Divisors	1, 73
Greek numeral	ΟΓ´
Roman numeral	LXXIII
Binary	10010012
Ternary	22013
Senary	201half-dozen
Octal	1118
Duodecimal	6112
Hexadecimal	49sixteen

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 [edit]

73 is the 21st prime number number, and emirp with 37, the 12th prime number.^[1] It is as well the eighth twin prime, with 71. It is the largest minimal primitive root in the offset 100,000 primes; in other words, if p is one of the first ane hundred one thousand primes, and then at least one of the numbers two, three, 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: 10 ⁴ + 1 = 10,001 = 73 × 137, and the smallest prime congruent to 1 modulo 24, as well as the only prime repunit in base eight (111₈). Information technology is the quaternary star number.^[2]

73 every bit a star number (upwards to blueish dots). 37, its dual permutable prime, is the preceding consecutive star number (upwardly to green dots) inside the sequence of star numbers.^[2]

Notably, 73 is the sole Sheldon prime to contain both mirror and product backdrop:^[3]

• 73, as an emirp, has 37 every bit its dual permutable prime, a mirroring of its base ten digits, 7 and iii. 73 is the 21st prime number, while 37 is the 12th, which is a 2d mirroring; and
• 73 has a prime index of 21 = vii x three; a product belongings where the product of its base-10 digits is precisely its alphabetize in the sequence of prime numbers.

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

73 + 21 = 94 (or, 47 × two),

37 + 12 = 49 (or, 47 + two = sevenⁱⁱ);

94 - 49 = 45 (or, 47 − ii).

Other backdrop ligating 73 with 37 include:

• 73 and 37 are lucky primes and sexy primes, both twice over.^{[4] [five] [vi]}
• 73 and 37 are sequent star numbers, respectively the 4th and the 3rd.^[2]
• 73 and 37 are consecutive values of ${\displaystyle g(chiliad)}$ such that every positive integer tin can exist written equally the sum of 73 or fewer 6th powers, or 37 or fewer fifth powers (meet Waring's problem).^[7]
• 73 and 37 are sequent primes in the 7-integer covering set up of the first known Sierpinski number 78,557, of the form ${\displaystyle k}$ x ${\displaystyle ii^{m}}$ + ${\displaystyle 1}$ composite for all natural numbers ${\displaystyle k}$ , with 73 as its largest group member: {3, five, 7, 13, 19, 37, 73}.

Consider the following sequence ${\displaystyle A(n)}$ :^[eight]

Let ${\displaystyle k}$ be a Sierpiński number or Riesel number divisible by ${\displaystyle 2n}$ − ${\displaystyle 1}$ , and permit ${\displaystyle p}$ exist the largest number in a set of primes which cover every number of the form ${\displaystyle chiliad*2^{one thousand}}$ + ${\displaystyle one}$ or of the form ${\displaystyle thousand*ii^{m}}$ − ${\displaystyle 1}$ , with ${\displaystyle m}$ ≥ 1;

${\displaystyle A(north)}$ equals ${\displaystyle p}$ iff there exists no number ${\displaystyle thousand}$ that has a covering ready with largest prime greater than ${\displaystyle p}$ .

Known such index values ${\displaystyle n}$ where ${\displaystyle p}$ is equal to 73 as the largest member of such covering sets are: {1, six, 9, 12, 15, xvi, 21, 22, 24, and 27}, with 37 present alongside 73. In particular, ${\displaystyle A(n)}$ ≥ 73 for any ${\displaystyle n}$ .

• 73 and 37 take a range of 37 numbers, inclusive of both 37 and 73; their deviation, on the other manus, is 36, or thrice 12.

${\displaystyle 777}$ = ${\displaystyle 3}$ x ${\displaystyle 37}$ x ${\displaystyle vii}$ = ${\displaystyle 21}$ x ${\displaystyle 37}$ , where 37 is a concatenation of iii and 7.

${\displaystyle 703}$ is equal to the sum of the first 37 non-zero integers, equivalently the 37^th triangular number.^[9] Its harmonic hateful is ${\displaystyle 3.7}$ .

${\displaystyle 373}$ has a prime alphabetize of 74, or twice 37.^[10] Like 73 and 37, 373 is a permutable prime alongside ${\displaystyle 337}$ and ${\displaystyle 733}$ , the second of three trios of iii-digit permutable primes in decimal.^[11] ${\displaystyle 337}$ is also the eighth star number.^[2]

${\displaystyle 337}$ + ${\displaystyle 373}$ + ${\displaystyle 733}$ = ${\displaystyle 1443}$ , the number of edges in the bring together of two wheel graphs of social club 37.^[12]

${\displaystyle 343}$ = ${\displaystyle seven}$ x ${\displaystyle 7}$ x ${\displaystyle 7}$ = ${\displaystyle 7}$ ³ , the cube of seven or equivalently 7 cubed, wherein replacing 2 neighboring digits with their digit sums ${\displaystyle 3}$ + ${\displaystyle 4}$ and ${\displaystyle iv}$ + ${\displaystyle three}$ yields ${\displaystyle 3{\mathbf {seven}}}$ : ${\displaystyle {\mathbf {7}}3}$ .

Also, the product of neighboring digits ${\displaystyle 3}$ 10 ${\displaystyle iv}$ is ${\displaystyle 12}$ , like ${\displaystyle 4}$ x ${\displaystyle 3}$ , while the sum of its prime factors ${\displaystyle vii}$ + ${\displaystyle 7}$ + ${\displaystyle 7}$ is ${\displaystyle 21}$ .

${\displaystyle 307}$ has a prime index of 63, equal to thrice 21. ${\displaystyle 3}$ x ${\displaystyle 3}$ x ${\displaystyle vii}$ , equivalently ${\displaystyle iii}$ 10 ${\displaystyle 7}$ x ${\displaystyle iii}$ and ${\displaystyle 7}$ x ${\displaystyle three}$ x ${\displaystyle iii}$ , are all permutations of the prime factorization of ${\displaystyle 21}$ .

• In moonshine theory of sporadic groups, 73 is the first non-supersingular prime number greater than 71. All primes greater than or equal to 73 are non-supersingular, while 37, on the other hand, is the smallest prime that is not supersingular.^[13]

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 three ones. In addition to having prime factors vii and 3, the number 21 represents the ternary (base-three) equivalent of the decimal numeral 7, that is to say: 21₃ = vii_ten.

73 is the largest member of the ${\displaystyle 17}$ -integer matrix definite quadratic that represents all prime numbers: {ii, 3, v, seven, xi, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 67, ${\displaystyle {\mathbf {73}}}$ }.^[14]

In science [edit]

• The atomic number of tantalum

In astronomy [edit]

• 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 Infinite Shuttle Challenger OV-099 shuttle to explode afterward launch.
• 73 is the number of rows in the 1,679-flake Arecibo bulletin, sent to infinite in search for extraterrestrial intelligence.

In chronology [edit]

• The yr Advert 73, 73 BC, or 1973.
• The number of days in ane/v of a not-leap year.
• The 73rd day of a non-bound year is March fourteen, also known as Pi Twenty-four hour period.

In other fields [edit]

73 is also:

• The number of books in the Catholic Bible.^[15]
• Amateur radio operators and other morse lawmaking users normally use the number 73 as a "92 Code" abbreviation for "best regards", typically when ending a QSO (a conversation with another operator). These codes likewise facilitate advice betwixt operators who may not be native English language speakers. [1] In Morse code, 73 is an easily recognized palindrome: ( - - · · · · · · - - ).
• 73 (as well known as 73 Amateur Radio Today) was an apprentice radio magazine published from 1960 to 2003.
• 73 was the number on the Torpedo Patrol (PT) boat in the Idiot box testify McHale'southward Navy.
• The registry of the U.S. Navy's nuclear shipping carrier USSGeorge Washington(CVN-73), named later on U.S. President George Washington.
• No. 73 was the name of a 1980s children's television programme in the United Kingdom. Information technology ran from 1982 to 1988 and starred Sandi Toksvig.
• Pizza 73 is a Canadian pizza concatenation.
• Game show Friction 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 [edit]

• In international curling competitions, each side is given 73 minutes to complete all of its throws.
• In baseball, the unmarried-season dwelling house run tape ready past Barry Bonds in 2001.
• In basketball game, the number of games the Golden State Warriors won in the 2015–xvi season (73-nine), the almost wins in NBA history.
• NFL: In the 1940 NFL championship game, the Bears beat the Redskins 73–0, the largest score always in an NFL game. (The Redskins won their previous regular season game, vii–3).

See also [edit]

• List of highways numbered 73

References [edit]

1. ^ "Sloane'due south A006567 : Emirps". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29 .
2. ^ ^{a b c d} "Sloane's A003154 : Centered 12-gonal numbers. Also star numbers: 6*n*(n-1) + 1". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29 .
3. ^ Pomerance, Carl; Spicer, Chris (Feb 2019). "Proof of the Sheldon theorize" (PDF). American Mathematical Monthly. 126 (eight): 688–698. doi:ten.1080/00029890.2019.1626672.
4. ^ Sloane, N. J. A. (ed.). "Sequence A031157 (Numbers that are both lucky and prime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-x-fourteen .
5. ^ Sloane, N. J. A. (ed.). "Sequence A023201 (Primes p such that p + 6 is also prime. (Bottom of a pair of sexy primes.))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-10-xiv .
6. ^ Sloane, North. J. A. (ed.). "Sequence A046117 (Primes p such that p-6 is also prime. (Upper of a pair of sexy primes.))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-10-14 .
7. ^ Sloane, N. J. A. (ed.). "Sequence A002804 ((Presumed) solution to Waring'due south problem)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
8. ^ Sloane, North. J. A. (ed.). "Sequence A305473 (Let k be a Sierpiński or Riesel number divisible past ii*n - 1...)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-ten-thirteen .
9. ^ Sloane, Due north. J. A. (ed.). "Sequence A000217 (Triangular numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-ten-13 .
10. ^ Sloane, North. J. A. (ed.). "Sequence A000040 (The prime number numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-10-thirteen .
11. ^ Sloane, N. J. A. (ed.). "Sequence A003459 (Absolute primes (or permutable primes): every permutation of the digits is a prime number.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-ten-xiii .
12. ^ "Sloane's A005563 : a(n) = n*(n+2) = (north+i)^2 - one". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-x-15 . Number of edges in the bring together of ii cycle graphs, both of order northward, C_n * C_n.
13. ^ Sloane, North. J. A. (ed.). "Sequence A002267 (The 15 supersingular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-10-xiii .
14. ^ Sloane, N. J. A. (ed.). "Sequence A154363 (Numbers from Bhargava'due south prime-universality benchmark theorem)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
15. ^ "Catholic Bible 101". Catholic Bible 101 . Retrieved 16 September 2018.

73 Is A Prime Number,

Source: https://en.wikipedia.org/wiki/73_(number)

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