37 (number)
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37 is a natural number that comes between 36 and 38. It is an odd number and also a prime number—meaning it is divisible only by 1 and itself. In Roman numerals it is written XXXVII, and in binary notation it is written 100101.
37 is notable for its relationship with repeating-digit numbers such as 111 and 999. Since 111 = 3 × 37, every three-digit number with identical digits (111, 222, 333 ... 999) is divisible by 37. This property makes 37 important in the divisibility methods of base-ten arithmetic.
Place among prime numbers
37 is the 12th prime number counting from 2. It is also an emirp—when its digits are reversed, 73 is obtained, which is also prime. Additionally, 37 is classified as a Cuban prime, a type that arises from the difference of two consecutive cubes.
Other mathematical properties
37 can be expressed as 6² + 1, making it expressible as a sum of two squares: 1 + 36. It is also among the centered hexagonal numbers—the sequence 1, 7, 19, 37—which arise when hexagons are successively layered around a central point.
General use
37 is used as an ordinary numeral and reference number in contexts such as dates, road numbers, and components of numbering systems. Like other small numbers, it is often employed in mathematics education to demonstrate divisibility and the properties of prime numbers.