Changes: 3

Revision as of 20:40, 8 January 2020

3

Basic Information

Cardinal Number

three

Ordinal Number

third

Roman Numeral

III

Greek Numeral

Γ´

Factorization

3

Different Representations

Binary Form

11₂

Ternary Form

10₃

Quaternary Form

3₄

Quinary Form

3₅

Senary Form

3₆

Septenary Form

3₇

Octal Form

3₈

Nonary Form

3₉

Undecimal Form

3₁₁

Duodecimal Form

3₁₂

Tridecimal Form

3₁₃

Quattuordecimal Form

3₁₄

Quindecimal Form

3₁₅

Hexadecimal Form

3₁₆

Septendecimal Form

3₁₇

Octodecimal Form

3₁₈

Novemdecimal Form

3₁₉

Vigesimal Form

3₂₀

Unvigesimal Form

3₂₁

Duovigesimal Form

3₂₂

Trevigesimal Form

3₂₃

Quattuorvigesimal Form

3₂₄

Quinvigesimal Form

3₂₅

Hexavigesimal Form

3₂₆

Septenvigesimal Form

3₂₇

Octovigesimal Form

3₂₈

Novemvigesimal Form

3₂₉

Trigesimal Form

3₃₀

Untrigesimal Form

3₃₁

Duotrigesimal Form

3₃₂

Tretrigesimal Form

3₃₃

Quattuortrigesimal Form

3₃₄

Quintrigesimal Form

3₃₅

Hexatrigesimal Form

3₃₆

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2	3	5

3 is the second prime number and the second single digit prime number. 3's prime factors are 1 and 3. It is said to be the first odd prime, because the previous prime number is 2, which is even.

It is also the first Fermat prime and the first Mersenne Prime.

Proofs

— 3 can be divided by 1.

— 3 cannot be divided by 2.

— 3 can be divided by 3.

Therefore, it has 2 factors.

As an Exponent of Mersenne Number

$2^3-1$ , which is the number 7, is a prime number. It is the 2nd Mersenne Prime.

Relationship with other numbers

The numbers before

2 is the first prime number. It is the only even prime number.
1, the number before 2, is not a prime number.

The numbers after

The next number, 4, is the first composite number, and a square number. It is the square of 2.
The next odd number, 5, is a prime number.
- There are no odd numbers between 3 and 5, and they are two numbers apart. As a result, they are twin primes.
7, the odd number following 5, is a prime number.
- 3 and 7 are four numbers apart, therefore, they are cousin primes.
9, the odd number following 7, is not a prime number. It is a square number and the first odd composite number.

Usage

General

Trilogy refers to a set of three works of art that are connected, either as a single work or three individual works.

Science

Lithium's atomic number and the number of electrons are 3.
Tritium (hydrogen-3) has a nucleon number of 3.

Sports

In basketball, a shot behind the three-point arc is worth three points, unless in the 3x3 variant.
In baseball, 3 strikes are required for the player to be considered "out", and 3 outs are required for the attacking team to exchange with the opposing team.

Video Games

In The Legend of Zelda series, there is a sacred relic called Triforce, which consists of three separate golden triangles.

Prime Numbers 1-1,000

1-100
1-25	2 • 3 • 5 • 7 • 11 • 13 • 17 • 19 • 23
26-50	29 • 31 • 37 • 41 • 43 • 47
51-75	53 • 59 • 61 • 67 • 71 • 73
76-100	79 • 83 • 89 • 97

101-200
101-125	101 • 103 • 107 • 109 • 113
126-150	127 • 131 • 137 • 139 • 149
151-175	151 • 157 • 163 • 167 • 173
176-200	179 • 181 • 191 • 193 • 197 • 199

201-400
201-250	211 • 223 • 227 • 229 • 233 • 239 • 241
250-300	251 • 257 • 263 • 269 • 271 • 277 • 281 • 283 • 293
301-350	307 • 311 • 313 • 317 • 331 • 337 • 347 • 349
351-400	353 • 359 • 367 • 373 • 379 • 383 • 389 • 397

401-600
401-450	401 • 409 • 419 • 421 • 431 • 433 • 439 • 443 • 449
450-500	457 • 461 • 463 • 467 • 479 • 487 • 491 • 499
501-550	503 • 509 • 521 • 523 • 541 • 547
551-600	557 • 563 • 569 • 571 • 577 • 587 • 593 • 599

601-800
601-650	601 • 607 • 613 • 617 • 619 • 631 • 641 • 643 • 647
651-700	653 • 659 • 661 • 673 • 677 • 683 • 691
701-750	701 • 709 • 719 • 727 • 733 • 739 • 743
751-800	751 • 757 • 761 • 769 • 773 • 787 • 797

801-1,000
801-850	809 • 811 • 821 • 823 • 827 • 829 • 839
851-900	853 • 857 • 859 • 863 • 877 • 881 • 883 • 887
901-950	907 • 911 • 919 • 929 • 937 • 941 • 947
951-1000	953 • 967 • 971 • 977 • 983 • 991 • 997

@@ Line 9: / Line 9: @@
 |Base-8 Form = 3
 |Base-16 Form = 3
-|previous = [[2|<font color="white">2</font>]]
+|previous = 2
-|next = [[5|<font color="white">5</font>]]}}
+|next = 5}}
+'''3''' is the second prime number and the second single digit prime number. 3's prime factors are 1 and 3. It is said to be the first odd prime, because the previous prime number is [[2]], which is even.
-is the second prime number, and the second single digit prime number. 3's prime factors are 1 and 3. It is said to be the first odd prime, because the previous prime number is [[2]], which is even.
 It is also the first [[Fermat Primes|Fermat prime]] and the first [[Mersenne Prime]].
 ==Proofs==
-*{{Divisibility number|Yes|1}}
+*{{Divisibility number|Yes|1.}}
-*{{Divisibility number|Yes|3}}
+*{{Divisibility number|No|2.}}
+*{{Divisibility number|Yes|3.}}
-*Therefore it has 2 factors, not 3, because 3 divided by 2 does not result in an [[integer]] value.
+*Therefore, it has 2 factors.
+==As an Exponent of Mersenne Number==
-==Relationship with other odd numbers==
+<math>2^3-1</math>, which is the number [[7]], is a prime number. It is the 2nd Mersenne Prime.
+==Relationship with other numbers==
 ===The numbers before===
-*2 is the first prime number. It is the only '''even''' prime number.
+*[[2]] is the first prime number. It is the only '''even''' prime number.
-*'''1''', the number before 2, is '''not '''a prime number.
+*'''1''', the number before 2, is '''not''' a prime number.
 ===The numbers after===
+*The next number, 4, is the first composite number, and a square number. It is the square of 2.
 *The next odd number, [[5]], is a prime number.
-**There are no odd numbers between 3 and 5. As a result, they are twin primes.
+**There are no odd numbers between 3 and 5, and they are two numbers apart. As a result, they are [[Twin Primes|twin primes]].
 *[[7]], the odd number following 5, is a prime number.
-**3 and 7 are four numbers apart, therefore, they are cousin primes.
+**3 and 7 are four numbers apart, therefore, they are [[Cousin Primes|cousin primes]].
-*9, the odd number following 7, is not a prime number. It is a square number, and the first odd composite number.
+*9, the odd number following 7, is not a prime number. It is a square number and the first odd composite number.
 ==Usage==
 ===General===
-* Trilogy refers to a set of three works of art that are connected, either as a single work or three individual works.
+*Trilogy refers to a set of three works of art that are connected, either as a single work or three individual works.
 ===Science===
-*Lithium's atomic number and number of electrons are 3.
+*Lithium's atomic number and the number of electrons are 3.
+*Tritium (hydrogen-3) has a nucleon number of 3.
-*Group three elements also have the valence of +3. Similarly, group five elements have the valence of -3.
-*Tritium / hydrogen-3, has a nucleon number of 3.
 ===Sports===
 *In basketball, a shot behind the three-point arc is worth three points, unless in the 3x3 variant.
-* In baseball, 3 strikes are required for the player to be considered "out", and 3 outs are required for the attacking team to exchange with the opposing team.
+*In baseball, 3 strikes are required for the player to be considered "out", and 3 outs are required for the attacking team to exchange with the opposing team.
 ===Video Games===
 *In The Legend of Zelda series, there is a sacred relic called Triforce, which consists of three separate golden triangles.
@@ Line 48: / Line 50: @@
 [[tl:3]]
 {{Navbox primes}}
-[[Category:Prime numbers from 1-100| 3]]
+[[Category:Prime numbers from 1-100|03]]
-[[Category:Prime Numbers]]
+[[Category:Prime Numbers|0003]]
 [[Category:1-Digit Prime Numbers]]
 [[Category:Twin Primes]]
@@ Line 57: / Line 59: @@
 [[Category:Additive Primes]]
 [[Category:Fibonacci Primes]]
+[[Category:Cousin Primes]]
+[[Category:Factorial Primes]]
+[[Category:Palindromic Primes]]
+[[Category:Chen Primes]]