Sixty-seven is the integer that follows sixty-six and precedes sixty-eight. It is an odd whole number and an prime number, meaning it has no positive divisors other than 1 and itself. In the sequence of prime numbers 67 is the 19th.

Mathematical properties

As a prime, 67 plays the usual role in number theory as an indivisible building block for integers. It is congruent to 3 modulo 4, which implies it cannot be expressed as a sum of two integer squares. It is also a Gaussian prime (a prime in the ring of Gaussian integers) because ordinary primes congruent to 3 mod 4 remain prime in that domain.

  • Prime index: 19th prime.
  • Modular forms: 67 ≡ 3 (mod 4) and ≡ 1 (mod 3).
  • Binary and hexadecimal: 67 in binary is 1000011 and in hex is 0x43.

67 can be written as 2^6 + 3, a simple exponential expression. It sits at the end of a prime gap of length six (between 61 and 67). Some specialized classifications from research identify 67 as a Chen prime because 67 + 2 is a product of two primes (a semiprime).

Science, computing and culture

In chemistry the atomic number 67 identifies the element holmium (Ho), a lanthanide used in certain magnetic alloys and lasers. In computing, the ASCII code 67 corresponds to the uppercase letter 'C'. In astronomy M67 (Messier 67) is a well-studied open star cluster in the constellation Cancer, notable for its age and rich stellar population.

Numerals like 67 also appear in everyday contexts—road numbers, model names and other labels—but their most lasting importance comes from the number's mathematical nature and its appearances in science. The English name "sixty-seven" derives from the regular decimal naming pattern (Latin roots reflected in some historical forms, e.g. Latin sexaginta septem), and its written symbols are the digits '6' and '7'.

Notable distinctions: 67 is a prime that is not a twin prime, not a safe prime, and is one of the primes congruent to 3 mod 4. Its simple binary and hexadecimal forms make it convenient in some low-level computing examples, while its role as the atomic number ties it to real-world materials science.