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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 31 in Username5243's Array Notation.