79 (number)

Seventy-nine is an odd prime integer, the 22nd prime, atomic number of gold, and a number with several mathematical and cultural connections, including Messier 79 and the AD 79 eruption of Vesuvius.

Overview

Seventy-nine is a natural integer that follows seventy-eight and precedes eighty. It is an odd number and, in the sequence of prime numbers, occupies the position of the 22nd prime. As a basic numeral it appears in arithmetic, counting and many indexing systems.

Mathematical properties

79 is a prime number: its only positive divisors are 1 and itself. It belongs to several prime-related categories. It is a Gaussian prime because it is a rational prime congruent to 3 mod 4, and it is an emirp (its digit reversal, 97, is also prime). The pair 79 and 83 form a cousin prime pair (difference 4), while 73 and 79 are separated by 6 and therefore form a sexy-prime pair; see nearby primes like 73 and 83.

Representations and notation

Decimal: 79
Binary: 1001111
Octal: 117
Hexadecimal: 0x4F
Roman numerals: LXXIX

History, science and culture

The number 79 appears outside pure mathematics in several notable places. In chemistry it is the atomic number of gold (Au), an element long associated with wealth and technology. In astronomy, Messier object M79 is a globular cluster cataloged by Charles Messier. Historically, the year AD 79 is widely cited as the date when Mount Vesuvius erupted, burying the Roman cities of Pompeii and Herculaneum, though the precise calendar date is subject to scholarly discussion.

Uses and notable facts

Because 79 is prime it is used in number-theory examples and cryptographic teaching (primes serve as building blocks for many algorithms). Its simple representations make it convenient for examples of base conversion, modular arithmetic, and primality demonstrations. For broader context, it sits between the concept of a natural number and larger composite or prime integers studied in arithmetic and algebra.