Nine (9) is a positive integer one more than 8 and one less than 10.

## PropertiesEdit

9 is the first odd composite number. It is also the first odd number more than 1 not to be prime . Instead, it is a semiprime number. 9 is the third square number, coming between 4 and 16.

9 is the fourth lucky number, between 7 and 13.

## In googology Edit

9 is also equal to !4 using subfactorial.

## In googology Edit

Some googologisms based on 9 are googolnoniplex and superenn.

9 can be named **mree** with the -ree series.

9 can be named "garthree" with the gar- prefix.

In Greek-based number naming systems, 9 is associated with prefix ennea-, and with prefix nona- or novem- in Latin systems

Donald Knuth calls this number **noniad**, and it's equal to using the -yllion system.

Since 9 is one less than our number base, testing for divisibility by nine is as simple as adding all the digits together, until you get a one-digit number. If it is nine, the original number is divisible by 9. For instance, 48735 is divisible by nine since the sum of its digits is 27, and the sum of 27's digits is 9.

Since 9 contains the prime 3 twice, a regular 9-sided polygon can't be constructed with a compass and straightedge.

9 and 8 are the only perfect powers differing by 1.

### Googological functions returning 9 Edit

- Gijswijt's sequence: \(c(3)=9\)
- Laver table: \(q(4)=9\)
- Mixed factorial: \(3^*=9\)
- Expostfacto function: \(\mathrm{expostfacto}(3)=9\)
- Exponential factorial: \(3!1=9\)