73 (seventy-three) is thenatural number following72 and preceding74. In English, it is the smallest natural number with twelve letters in its spelled out name.
Where 73 and37 are part of the sequence ofpermutable primes andemirps in base-ten, the number 73 is more specifically the uniqueSheldon prime, named as an homage to TV characterSheldon Cooper and defined as satisfying "mirror" and "product" properties, where:[3]
73 has 37 as the mirroring of itsdecimal digits. 73 is the 21st prime number, and 37 the 12th. The "mirror property" is fulfilled when 73 has a mirroredpermutation of its digits (37) that remains prime. Similarly, their respective prime indices (21 and 12) in thelist of prime numbers are also permutations of the same digits (1, and 2).
73 is the 21st prime number. It satisfies the "product property" since the product of its decimal digits is precisely in equivalence with its index in thesequence of prime numbers. i.e., 21 = 7 × 3. On the other hand, 37 does not fulfill the product property, since, naturally, its digits also multiply to 21; therefore, the only number to fulfill this property between these two numbers is 73, and as such it is the only "Sheldon prime".
73 and 37 are consecutive primes in the seven-integercovering set of the first knownSierpiński number 78,557 of the form that iscomposite for all natural numbers, where 73 is the largest member: More specifically,modulo36 will be divisible by at least one of the integers in this set.[citation needed]
Let be a Sierpiński number orRiesel number divisible by, and let be the largest number in a set of primes which cover every number of the form or of the form, with;
equalsif and only if there exists no number that has a covering set with largest prime greater than.
Known such index values where is equal to 73 as the largest member of such covering sets are:, with 37 present alongside 73. In particular, ≥ 73 for any.
In addition, 73 is the largest member in the covering set of the smallest provengeneralized Sierpiński number of the form innonary, while it is also the largest member of the covering set that belongs to the smallest such provable number indecimal — both in congruencies.[10][11]
Lah numbers for and between 1 and 4. The sum of values with and is73.
73 is one of the fifteen left-truncatable and right-truncatable primes indecimal, meaning it remains prime when the last "right" digit is successively removed and it remains prime when the last "left" digit is successively removed; and because it is a twin prime (with 71), it is the only two-digit twin prime that is both a left-truncatable and right-truncatable prime.
The row sum ofLah numbers of the form with and is equal to.[12] These numbers representcoefficients expressingrising factorials in terms of falling factorials, and vice-versa; equivalently in this case to the number ofpartitions of into any number of lists, where a list means anordered subset.[13]
73 requires 115 steps to return to 1 in theCollatz problem, and 37 requires 21: {37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2,1}.[14] Collectively, the sum between these steps is136, the 16th triangular number, where {16, 8, 4, 2, 1} is the only possible step root pathway.[15]
There are 73 three-dimensionalarithmetic crystal classes that are part of 230 crystallographic space group types.[16] These 73 groups are specificallysymmorphic groups such that all operating lattice symmetries have one common fixedisomorphicpoint, with the remaining157 groups nonsymmorphic (the 37th prime is 157).
73 is the largest member of a 17-integer matrixdefinite quadratic that represents allprime numbers: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,37, 41, 43, 47, 67,73},[19] with consecutive primes between2 through47.
73 is the ninth member of the sequence ofHogben's central polygonal numbers, which enumerates the maximal number of interior regions formed by nine intersecting circles.[20]
Amateur radio operators and othermorse code users commonly use the number 73 as a"92 Code" abbreviation for "best regards", typically when ending aQSO (a conversation with another operator). These codes also facilitate communication between operators who may not be native English speakers.[21] InMorse code, 73 is an easily recognized palindrome: ( - - · · · · · · - - ).
73 isSheldon Cooper's favorite number in the television seriesThe Big Bang Theory. He first expresses his love for it in episode 73, "The Alien Parasite Hypothesis" (2010).[22]Jim Parsons, who plays Cooper in the series, was born in1973.[23] His character often wears at-shirt with the number 73 on it.[24]
