# 73

This number is a prime.

The smallest multidigit prime partial sum of deficient numbers: 1 + 2 + 3 + 4 + 5 + 7 + 8 + 9 + 10 + 11 + 13 = 73 is prime. [Post]

π(73) = 7*3. [Honaker]

73 is the 37th odd number. [Hasler]

73! + 1 is prime. [Buhler , Crandall and Penk]

There are exactly 73 primes, beginning with the prime 1093 and ending
with the prime 1613, where 1093^{2} + 1097^{2} + ... + 1613^{2} = 11707^{2}.
This is the first instance of a prime number of primes comprising the left member of such an equation. [Haga]

Here's a neat trick with its digits: 7^{3} = 343 or (3 + 4)^{3}.

The smallest prime whose digits are reversed in base 22. [Haga]

The 2*p*-twin peak of height *p* = 73 is the smallest known *twin peak*. [Hoey]

The USS *George Washington* (CVN-73) currently has the largest prime hull number of any aircraft carrier in the American fleet.

The minimum number of sixth powers needed to represent every possible integer. [Pillai]

3^{12}/2^{19} ~ 1 + 1/73. [Littlewood]

Starting with 73, you must repeatedly double and add 1 a palindromic number of times before a prime is reached. [Roonguthai]

The smallest prime whose square (5329) is the concatenation of two multidigit primes. [Trotter]

389 and 17 are primes, as is their concatenation (38917). Inserting the lowly 0 between them transforms the prime into a power, i.e. 389017, the cube of 73, a prime itself. [Trotter]

The record number of major league home runs hit in one season is 73. Barry Bonds set it in 2001.

The space shuttle Challenger disaster occurred 73 seconds after liftoff.

The Empire State Building has 73 elevators.

The only known emirp which is 1 less than the double of its reversal. [Boggio]

The content editor of "Prime Curios!" is credited on page 73 of R. Crandall and C. Pomerance, *Prime Numbers: A Computational Perspective*, Springer-Verlag, NY, (2002 printing), with noting that 61 divides 67*71 + 1. [Haga]

The song "Ride, Captain, Ride" begins with "73 men sailed up from the San Francisco Bay, ..." [McCranie]

The number formed by the concatenation of odd numbers from 73 down to 1 is prime. [Patterson]

The prime number 73 is the repunit 111 in octal (base 8) and the palindrome 1001001 in binary (base 2). [Dobb]

It took Australian anatomy professor Raymond Dart 73 days to chisel the skull of Taung Child from its surrounding stone matrix. [O'Neil]

Pi Day (March 14 or 3/14) occurs on the 73rd day of the year on non-leap years. Howard Aiken died on Pi Day at the age of 73. He was the primary engineer behind IBM's Harvard Mark I computer. [Rupinski]

73 is the smaller prime factor of 10001. [Hartley]

The total number of books in the *Catholic Bible* if the Book of Lamentations is counted separate from the Book of Jeremiah. [Medine]

Thomas Jefferson and Aaron Burr each received 73 electoral votes and tied for the presidency.

(73!)/(73#)-1 is prime. [Patterson]

Gakuho Abe constructed a pair of magic squares using 73 consecutive prime numbers.

Manjul Bhargava showed that if a quadratic form represents all prime numbers up to 73, then it represents all prime numbers. [Poo Sung]

There are 73 composite numbers under 10^2. Proof: 73+25 primes = 98. There are 99 numbers under 10^2, but 1 is neither prime nor composite. This is the only instance of a prime count of composites through 10^22. [Haga]

The second prime Apéry number. [Post]

If A=1, B=2, C=3, ..., Z=26, then "NUMBER" is prime. [Speirs]

The largest two-digit prime n such that n!/reversal(n)+1 is prime. [Patterson]

A tropical storm is considered a hurricane if its sustained wind is higher than 73 miles per hour. [Wu]

The Maya, who came to prominence in the New World in the 3rd century A.D., used two calendars, based on a sacred year of 260 days and a vague year of 365 days. The least common multiple of the two calendars, called the calendar round, has 18980 days or 73 sacred years. [Dershowitz]

The success of the magazine known as *73 Amateur Radio
Today* gave Wayne Green the money to launch *Byte*
magazine. [Pierce]

The Discordian calendar has five 73-day seasons: Chaos, Discord, Confusion, Bureaucracy, and The Aftermath.

"My community will divide into 73 sects." Prophet Muhammad (circa 622).

73 is the amateur radio operator way of saying "best regards." [McCranie]

The number of rows in the Arecibo Message graphic. The Arecibo Message is a radio message that was sent toward a globular star cluster in Hercules from a radio telescope in Puerto Rico on November 16, 1974. The entire transmission lasted a semiprime number of seconds and provided a way for extraterrestrials to arrange a 73-by-23 array into recognizable data about our life and solar system.

The number of the PT boat in "McHale's Navy" is 73. [McCranie]

The first difficult prime to form under the rules of the four 4's puzzle. The problem is to find expressions for numbers using exactly four 4's and a finite number of mathematical symbols and operators in common use. One version of the rules allow only addition, subtraction, multiplication, division, square root, exponentiation, factorial, decimal point, parentheses, as well as concatenation. Here are two possible solutions (achieved by altering the rules above):

[Caldwell]

The sum of the first 73 odd primes is divisible by 73. [Seidov]

The smallest Apery emirp. [Loungrides]

The smallest prime that divides a 7-digit number of the
form *p*0*p*, where *p* is any 3-digit
prime. [Beedassy]

The largest integer with the property that all permutations of all its subsequences are primes. [Keith]

73 = 2^{3!} + 3^{2!}. [Silva]

The largest known prime that starts a chain (generated by
the quadratic 73 - *x* - *x*^{2}, for
*x* = 0, 1, 2, ... , 7) of smaller, increasingly
distant primes with successive gap 2*n*, (*n* =
1, 2, 3, ..., 7): 73, 71, 67, 61, 53, 43, 31, 17. [Beedassy]

The smallest prime factor of a googol + 1. [Poo Sung]

Huge Large Quasar Group (Huge-LQG) consists of 73 quasars.

Pizza 73 is a Canadian pizza chain. Customers can place orders using the internet.

The largest known prime number p such that
2^{p} does not contain the digit
1. [Capelle]

The largest known prime p such that p -
2^{k}, with p >
2^{k}, is prime or semiprime for
all k > 0. [Capelle]

The largest Scrabble value of "New Mexico." It is the largest possible prime value of all the US States. [Post]

The smallest prime with prime digits that belongs both to an emirp pair (37, 73) and to a twin prime pair (71, 73) as the larger member. [Beedassy]

73 is the only emirp that divides the maximum score of New Super Mario Bros. [Ducayet]

The record number of points scored by any National Football League team in a single game. (Bears beat Redskins 73-0 on December 8, 1940.)

The clepsydra (an ancient device that measured time by marking the regulated flow of water through a small opening) had a wheel with 73 teeth. [Robinette]

The smallest prime that is the middle term of three
consecutive numbers each expressible as a sum of two
nonzero squares: 72 = 6^{2} + 6^{2} ; 73 =
3^{2} + 8^{2} ; 74 = 5^{2} +
7^{2}. Note that replacing the first prime digit 7
by the prime 23 forms instead the smallest prime (233) that
is the middle term of three consecutive numbers each
expressible as a sum of two *distinct* nonzero
squares: 232 = 6^{2} + 14^{2} ; 233 =
8^{2} + 13^{2} ; 234 = 3^{2} +
15^{2}. [Beedassy]

Starting point of the first Smarandache-Wellin sequence by minimal decrements to have three primes other than itself, independent of whether the start is prime (7372717069, 73727170696867, and 737271...232221 are prime). [Merickel]

Smallest emirp partial sum of tetrahedron-tree numbers: 1 + 2 + 5 + 6 + 9 + 15 + 16 + 19 = 73. [Post]

73#+79 is the largest prime less than a googol of the form p#+q, where p, q are consecutive primes. [Loungrides]

There are 73 pairs of consecutive primes whose products have distinct digits. [Gaydos]

The best number according to Sheldon from the TV show "The Big Bang Theory." [Wright]

There are 73 non-isomorphic Jordan algebras. [Post]

There are 73 non-empty subsets of the digits 0-9 that cannot be the set of digits of a prime's decimal representation.

73 can be written as the sum of three distinct odd composite numbers in (7 minus 3) ways.

73 = 8^2 + 8^1 + 8^0. [Nwamba]

The 73rd triangular number is equal to 73 times the reversal of 73. [Bergot]

73 of the 216 possible rolls of three 6-sided dice total prime numbers. [Gaydos]

Removing the even digits from 2^73 leaves a prime number (973957399739) with 73 embedded in it three times. [Gaydos]

73 is the only
Sheldon prime, i.e., i) whose binary representation is
palindromic (1001001_{2}) and ii) which belongs to
an emirp pair (P_{n}, P_{m})
such that subscripts (*m*, *n*) = (21, 12) are
also reversals of each other and *n* has a prime
decomposition 21 = 3*7 that concatenates back to
P_{m} (Carl Pomerance, Chris Spicer,
February 2019). [Beedassy]

The smallest prime written as the sum of three distinct cubes: 1^3 + 2^3 + 4^3. [Leo]

73 is the gematria of wisdom (חכמה) in the Torah. [Slattery]

73*37 + 7^3 + 3^7 + 7*3 + 3*7 is a prime. [Bui Quang Tuan]

73 is the highest prime factor for 4273 of the first million composite numbers. 83 takes second place, being the highest prime factor for 4213 of the first million. 79 is third at 4211. [Gaydos]

There are 73 pseudoprimes in base seven less than ten thousand. [Homewood]

The biggest prime number whereas any decomposition of its figures in a new number is always prime (3, 7 and 37). [Bouton]

73 divides both 17!-1 and 71!-1. [Galliani]

73 is the concatenation (in decreasing order) of the first two Mersenne primes, 3 and 7. [Galliani]

73 = π(7^3 + 3^3). Note that 73 is the only known number with this property. [Bajpai]