Overview

47 is the integer that follows 46 and precedes 48. It is an odd number and, in the familiar base‑10 system, a prime: its only positive divisors are 1 and itself. As a small, simple integer it appears frequently in arithmetic examples and in cultural references.

Mathematical properties

In the ordered list of prime numbers, 47 is the 15th prime. Some of its basic arithmetic and number‑theoretic features include:

  • Prime status: divisible only by 1 and 47.
  • Safe prime: (47−1)/2 = 23 is also prime, so 47 is classified as a safe prime.
  • Congruences: 47 ≡ 3 (mod 4), which implies it cannot be expressed as a sum of two integer squares.
  • Digit sum: 4 + 7 = 11, itself a prime.
  • Representations in common bases: binary 101111, octal 57, hexadecimal 2F.

Notation and name

The written English name is "forty‑seven." In Roman numerals it is written XLVII. As with other small integers, its name and notation have evolved through Latin and Germanic influences into modern English forms used today.

Uses, examples and significance

Beyond pure mathematics, 47 appears in science and culture. Its most widely recognized scientific association is that it is the atomic number of the element silver (Ag). In popular culture it is also the subject of stories and media—most famously the historical tale of the Forty‑seven Ronin and modern fictional uses such as character identifiers in novels and games. In cryptography and group theory, safe primes like 47 serve as simple illustrative examples of primes that are useful in key‑exchange schemes, although practical systems require far larger primes.

Notable distinctions

47 sits between the composite numbers 46 and 48, and it is separated from the previous prime, 43, by a gap of four; such a pair (43, 47) is sometimes called "cousin primes." As a relatively small safe prime and a 3 (mod 4) prime, 47 often appears in textbook examples about quadratic residues, primality tests and modular arithmetic.

Further reading

For concise listings of its appearances in mathematics and culture, see introductory number theory texts and reference works on chemical elements and cultural history.