2567

2567 is a natural number that follows 2566 and precedes 2568. It is an odd integer and can be expressed as the product of two prime numbers: 17 × 151, making it a semiprime. Its prime factorization highlights that it has exactly four positive divisors: 1, 17, 151, and 2567 itself. The sum of these divisors equals 2746, and the sum of the proper divisors (excluding the number itself) is 179, indicating that 2567 is a deficient number.

In different numeral systems, 2567 has distinct representations: in binary it is 101000001111, in octal it is 5007, and in hexadecimal it appears as 0xA07. The number is also a palindromic prime in base 12, where it is written as 1811₁₂. When expressed in Roman numerals, 2567 is written as MMDLXVII.

Mathematically, 2567 is not a perfect square, cube, or any higher integer power. It is not a triangular, pentagonal, or Catalan number, but it does appear in the sequence of numbers that are the sum of two squares: 2567 = 38² + 27². Because both of its prime factors are congruent to 1 modulo 4, this representation follows from Fermat’s theorem on sums of two squares.

Outside pure mathematics, the integer 2567 is occasionally used as a model or catalog number in engineering and technology contexts, such as component identifiers or product codes. However, it does not hold particular cultural, historical, or scientific significance beyond its mathematical properties.