31 is a primorial prime.
31 is the largest number whose square contains all digits in descending order.
The integral parts of π3, 10π and 3π 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 googology Edit
In Greek-based number-naming systems, 31 is associated with prefix "hentriaconta-", and with prefix "untriginti-" in Latin systems.