73 is an integer that follows 72 and precedes 74. In elementary arithmetic it is a prime number, meaning its only positive divisors are 1 and itself. Beyond that basic fact, 73 has several curious relationships and representations that make it notable both inside mathematics and in broader culture.
Mathematical properties
As the 21st prime number, 73 participates in a neat numerical symmetry: its decimal reversal, 37, is the 12th prime, and the number 21 (the index of 73 among primes) equals the product of its decimal digits (7×3 = 21). Because its reversal is a different prime, 73 is classified as an emirp — a prime whose digit reversal is also prime. These layered relationships are often highlighted as elegant examples of digit-based coincidences.
Representations in other bases
73 has several notable representations when written in other numeral systems. In binary it is 1001001, which is palindromic (reads the same backward and forward). In octal it appears as 111, and in hexadecimal it is 49. These alternate forms are useful in computer science and number theory when exploring patterns that depend on base representation.
History, name and etymology
The English name "seventy-three" follows the standard pattern for two-digit numbers: tens word plus ones. Historically there is no unique origin story for the integer itself; instead it attains significance through the patterns people notice and the uses to which it has been put in science, technology and culture.
Uses, examples and cultural notes
Outside pure mathematics, 73 appears as the atomic number of the chemical element tantalum (Ta), a refractory metal important in electronics and capacitors. In amateur radio and telegraphy, the numeric shorthand "73" is a conventional valediction meaning "best regards." The number also received popular attention through its mention in contemporary media where enthusiasts celebrate its mathematical coincidences.
Notable facts and quick summary
- Prime status: 73 is prime (21st prime).
- Emirp: Its reversal 37 is prime, so 73 is an emirp.
- Digit product and index: 7×3 = 21, and 73 is the 21st prime.
- Binary palindrome: 73 = 1001001_2, a binary palindrome.
- Other bases: octal 111, hexadecimal 49.
- Scientific/cultural: atomic number of tantalum; "73" used as "best regards" in ham radio.
These interlocking numeric properties and real-world uses make 73 an often-cited example in recreational mathematics and everyday shorthand, illustrating how a simple integer can connect patterns, notation systems, elements and social convention.