- 31 is an odd prime number. It is a Mersenne prime, since it is equal to 25-1.
- 31 is a primorial prime.
- 31 is the largest number whose square contains all digits in descending order.
Relation to pi
- The integral parts of π3, 10π, 3π and 100/π are all equal to 31.
- The number π3 is almost equal to 31. The emphasis is on "almost", since π is a transcendental number.
In Greek-based number-naming systems, 31 is associated with prefix "hentriaconta-", and with prefix "untriginti-" in Latin systems.
- OEIS, Sequence A000668