| 3 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Numbers 0 - 99 | |||||||||
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 |
| 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
| 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 |
| 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 |
| 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 |
| 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 |
| 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 |
| 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 |
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]
- In SAN, hyp_cos uses the number 3 to name googolisms.
Googological functions returning 3[]
- Xi function: \(\Xi(3)=3\)
- Goodstein function: \(G(2)=3\)
- Weak Goodstein function: \(g(2)=3\)
- Kirby-Paris hydra: \(\text{Hydra}(2)=3\)
- TREE function: \(\text{TREE}(2)=3\)
- Fusible numbers: \(m_1(1) = 3\)
- gag: \(gag(1) = 3\)
- mag: \(mag(1) = 3\)
- Laver table: \(q(2)=3\)
- Gijswijt's sequence: \(c(2)=3\)
- Block subsequence theorem: \(n(1)=3\)
- Beklemishev's worms: \(\text{Worm}(1) = 3\)
- Mixed factorial: \(2^*=3\)
- H function: \(H(1)=3\)
- S function (both variants): \(S(1)=3\)
- U function: \(U(1)=3\)
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[]
Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · garmillion · gargoogol · gareceton · gartrialogue · gargoogolplex · gargiggol
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fztwenty · fzhundred · fzthousand · fzmillion · fzgoogol · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgargantugoogolplex · fzgiggol
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagargantugoogolplex · fugagiggol
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex · megafugagrangol
Extensions:
Booga-:: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaten · boogahundred · boogagoogol · boogagoogolplex
Gag-:: gagone · gagtwo · gagthree · gagfour · gagfive · gagsix · gagseven · gageight · gagnine · gagten · gaggoogol · gaggoogolplex
Megoogol · Meg-Googol · Meg-Doogol · Meg-Kiloogol · Meg-Kil-Googol · Meg-Dukiloogol · Meg-Trukiloogol · Dumegoogol · Dumeg-Googol · Dumeg-Kiloogol · Dumeg-Dukiloogol · Trumegoogol · Trumeg-Kiloogol · Tetrumegoogol · Pentumegoogol · Gigoogol · Gig-Googol · Gig-Kiloogol · Gig-Megoogol · Dugigoogol · Trugigoogol · Teroogol · Duteroogol · Truteroogol · Petoogol · Ectoogol · Zettoogol · Yottoogol · Xennoogol · Wekoogol
Note: The readers should be careful that numbers defined by Username5243's Array Notation are ill-defined as explained in Username5243's Array Notation#Issues. So, when an article refers to a number defined by the notation, it actually refers to an intended value, not an actual value itself (for example, a[c]b = \(a \uparrow^c b\) in arrow notation). In addition, even if the notation is ill-defined, a class category should be based on an intended value when listed, not an actual value itself, as it is not hard to fix all the issues from the original definition, hence it should not be removed.