4

4 (four) is a positive integer following 3 and preceding 5. Its ordinal form is written "4th" or "fourth".

Properties
4 is a, and the first with this property. 4 is an. 4 is the 2nd. 4 is the 2nd Busy Beaver number. Plugging 2 into the hyper operators degenerates to 4: \(2 \uparrow\uparrow ... \uparrow\uparrow 2 = 4\).

4 is associated with bad luck in Eastern numerology because the Chinese word for "four" sounds similar to the word for "death."

It is possible to test for divisibility by 4 in base 10 by looking at last 2 digits of the number. If the 2-digit number is divisible by 4, then the whole number is.

In googology
Some googologisms based on 4 are supertet, quadroogol and googolquadriplex. 4 can be thought as zeroth term of sequence defining Graham's number: \(g_0\) = 4.

In Greek-based number naming systems, 4 is associated with prefix tetra-, and with prefix quadri- in Latin systems.

4 can be named gartwo, fztwo, fugatwo, megafugatwo, or boogatwo with the gar-, fz-, fuga-, megafuga-, and booga- prefixes respectively.

Aarex Tiaokhiao calls this number binary-booiol.

Username5243 calls this number Binary-Goodol, and it's equal to 2[1]2 in Username5243's Array Notation.

Googological functions returning 4

 * Rado's Sigma Function: \(\Sigma(2)=4\)
 * Xi function: \(\Xi(4)=4\)
 * Hyperfactorial: \(H(2)=4\)