Overview

Thirty-seven is the integer after thirty-six and before thirty-eight. As a member of the positive integers it is commonly written 37 and is classified as an odd number. It is also a prime: its only positive divisors are 1 and itself. In the ordered list of primes 37 appears as the twelfth such number; see notes on primality below and prime number references for general context.

Mathematical properties

Key arithmetic properties of 37 include:

  • Prime status: 37 has no nontrivial factors.
  • Centered hexagonal number: 37 is the fourth centered hexagonal number (it fits the pattern 1, 7, 19, 37, ...).
  • Emirp: reversing its decimal digits gives 73, which is also prime; such primes that yield a different prime when reversed are called emirps.
  • Decimal repetition patterns: 37 has simple relations with repdigits — for example 3×37 = 111 and 27×37 = 999, so certain multiples of 37 produce repeated-digit numbers.

Patterns and examples

Because 37 divides 111 and 999, it appears in a range of elementary tricks and puzzles. Multiplying 37 by successive multiples of 3 yields repdigit sequences (3×37 = 111, 6×37 = 222, 9×37 = 333, …, 27×37 = 999). Its reversal, 73, provides a simple example of digit reversal symmetry in prime numbers.

Occurrences and uses

Beyond pure number theory, 37 appears as the atomic number of the chemical element rubidium, which connects the integer to chemistry and materials science. The number shows up in coding puzzles, calendar curiosities and recreational mathematics because of its compact, teachable patterns.

Further reading and distinctions

For broader context about integers and parity see general articles on the concept of a number and on odd versus even numbers. For properties of primes and centered figurate numbers consult resources on prime sequences and polygonal/centered numbers. The modest size of 37 makes it a convenient example when teaching divisibility, digit patterns, and basic prime-related ideas.