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3 (three) is a positive integer following 2 and preceding 4. Its ordinal form is written "third" or "3rd".

## Properties

3 is an odd prime number, the smallest number with both of those properties. It is a Fermat prime 220 + 1 and a Mersenne prime 22 - 1 and is the only number with both of these properties. 3 is the 2nd triangular number.

In base 10, it is easy to test for divisibility by 3 by simply summing the digits of the number. The result will be the same modulo 3, so the process may be repeated. This is a consequence of 10 being one more than a multiple of 3.

In base 10, 3 is the only Mersenne prime ending in 3. All the other Mersenne primes end in either 1 or 7.

Three is the base of the ternary numeral system, also known as trinary.

## In googology

BEAF arrays based on the number 3 are not degenerate, so Jonathan Bowers often coins googologisms based on this number. Some examples are tritri, tetratri, and dupertri. As the numbers get larger, their last digits converge to a single, very long string ending in $$...2,464,195,387$$ (see moduli of power towers).

In Greek- and Latin-based number naming systems, 3 is associated with prefix tri- (often shortened to tr-). For instance, the third -illion is called trillion.

André Joyce used the Mayan word "ox", meaning 3, in some of his googologisms.

Username5243 coined the name Ternary-Goonol for this number, and it's equal to 3[1]1 in Username5243's Array Notation.[1]

## As a cash denomination

Some currencies, such as the Bahamian dollar and the Uzbekistani soʻm, have banknotes with this number in the denomination.

Some currencies, such as the Cuban peso and the Tajikistani somoni, have coins with this number in the denomination.

## Sources

1. Part 1 - My Large Numbers