Overview

89 is a natural integer that comes after eighty-eight and before ninety. It is a positive whole number frequently encountered in counting, indexing and basic arithmetic. As a two-digit integer it has several simple representations and cultural uses that appear across science and recreational mathematics.

Mathematical properties

In number theory 89 is notable for being a prime number: it has no positive divisors other than 1 and itself. More precisely it is the 24th prime. The nearest primes are the preceding prime eighty-three and the following prime ninety-seven. Its basic representations include binary 1011001 and hexadecimal 0x59; in Roman numerals it is written LXXXIX.

  • Prime index: 24 (so 89 is the 24th prime).
  • Factorization: 1 × 89 (prime).
  • Digital sum: 8 + 9 = 17.
  • Binary: 1011001; Hexadecimal: 59.

89 is the 11th number in the Fibonacci sequence (..., 34, 55, 89, 144, ...). Because it is both prime and a Fibonacci number it is called a Fibonacci prime. It is the largest Fibonacci number with two decimal digits and is of interest in studies that examine overlaps between prime sequences and linear recurrence sequences.

Occurrences, examples and uses

The number 89 appears as the atomic number of the chemical element actinium (Ac), placing it in discussions of the periodic table and nuclear chemistry. In recreational mathematics 89 is noteworthy for being the sum of a run of consecutive primes: 11 + 13 + 17 + 19 + 29 = 89. Because it is prime, 89 is occasionally used in elementary examples of primality testing, modular arithmetic and simple cryptographic demonstrations (though it is far too small for real-world security).

Notable facts and distinctions

Beyond its roles above, 89 is a compact example that links different areas of elementary number theory—primality, Fibonacci structure and representations in base systems—making it a useful illustrative integer in teaching and puzzles. Its Roman numeral form LXXXIX is palindromic in structure of symbols, and it frequently appears in lists of interesting small primes used for examples and exercises.

For further reading on primes and Fibonacci numbers consult general references on integer sequences and introductory number theory texts. You may follow related topics via these links: prime numbers, and the neighboring integers referenced above.