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. 4 is the 2nd superperfect 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.
*Ignoring weekdays, the repeats every 4 years.
*Its Roman numeral is most commonly IV, but on clock faces, IIII is also used.
*Its prime factorization is 4 = 2².
*All known multiperfect numbers > 6 are divisible by 4.
*Base four, sometimes used as a way of compressing binary, is called .
== 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 coined the name binary-booiol or binary-golsol for this number, as s(2,100,1,2) = s(2,2,100,1) = s(2,2,100) in strong array notation.Part 1 (LAN) - Aarex Googology
*Username5243 coined the names Binary-Goodol and Binary-Goonolplex for this number, and it's equal to 2[1]2 = 2[1]2[1]1 in Username5243's Array Notation.Part 1 - My Large Numbers
*HaydenTheGoogologist2009 coined the mane binary-goobol for this number, and it's equal to \(\{2,100(1)2\}\) in BEAF.Hayden's Big Numbers - Goobol series. Retrieved 2022-09-26.
== Googological functions returning 4 ==
*Rado's Sigma Function: \(\Sigma(2)=4\)
*Xi function: \(\Xi(4)=4\)
*Hyperfactorial: \(H(2)=4\)
*Factorexation: \(2\,\backslash=4\)
*Superfactorial: (Clifford Pickover): \(2\$=4\)
*Graham sequence: \(G_{0}\) = 4
== Sources ==
cs:4
es:4
Category:Numbers
Category:Calendar-related numbers
Category:Class 0
Category:Powers of 2
Category:Gar-
Category:Fz-
Category:Fuga-
Category:Megafuga-
Category:Booga-
Category:Googol Regiment
Category:Doogol Regiment
Category:Toogol Regiment