# The Number 31: Properties and Meanings

**31** is a

Prime Number.

**31** is a

Mersenne Number.

**31** is a

Centered Triangular Number.

**31** is a

Centered Pentagonal Number.

**31** is a

Centered Decagonal Number.

There are only

**31** numbers which cannot be expressed as the sum of distinct squares.

**31** is the number of moves required in a Tower of Hanoi Puzzle containing

5 discs.

**31** can be

Partitioned 6842 ways.

**31** can be

Partitioned 16 times with each term no larger than

2
**31** can be

Partitioned 96 times with each term no larger than

3
**31** can be

Partitioned 321 times with each term no larger than

4
**31** can be

Partitioned 748 times with each term no larger than

5
**31** can be

Partitioned 1360 times with each term no larger than

6
The number of regular polygons with an odd number of sides that can be constructed with straightedge and compass =

**31**.

The

Chemical Element Gallium has an atomic number of

**31**.

The

Chemical Element Phosphorus has one

Stable Isotope. It has

**31** neutrons.

Pradjapati created the universe by articulating the odd numbers from

1 to

**31**, according to the Vajasaneya Samhita - white Yajur.

In Buddhism, there are

**31** planes of existence.

### The Year 31 AD

In the year

**31** AD Musonius Rufus, Roman philosopher was born.

In the year

**31** AD Saint Stephen died, by stoning.