3

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
Previous	2
Current	3
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 the first odd prime since the only even prime number is 2.

It is also the first Fermat prime, the first pi-prime number, the first prime of the form floor, and the first Mersenne prime. The primorial of 3 is 6.

Proofs

• — 3 is divisible by 1.

• — 3 is not divisible by 2.

An odd number can't be divisible by an even number.

• — 3 is divisible by 3.

• Therefore, it has 2 factors and is prime.

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 natural number before 2, is not a prime number, for if the primes included 1, then the factorization of a natural number n into a product of primes would not be unique, since n = n*1.

The numbers after

• The next natural number, 4, is the first composite number and the first non-trivial square number: 2².
• The next natural number, 5, is a prime number.
  • There are no odd numbers between 3 and 5, and the difference between 3 and 5 is 2. As a result, they are twin primes.
• 6 the natural number following 5 is the second composite number, first perfect number, and first composite number not square, 2*3.
• 7, the natural number following 6, is a prime number.
  • The difference between 7 and 3 is 4. Therefore, they are cousin primes.
• 8, the natural number following 7 is the third composite number, and the first non-trivial cube number 2³
• 9, the natural number following 8, is not a prime number. It is a square number and the first odd composite number, and generally fourth 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.
• 3 is the number of dimensions humans can perceive. Some theories suggest that there are more than 3 actual dimensions of the Universe.
• Each proton or neutron is composed of 3 quarks in particle physics.
• There are 3 primary colors in both the additive and subtractive models:
  • In the additive model, red, green, and blue are the primary colors (RGB).
  • In the subtractive model, cyan, magenta, and yellow are the primary colors (CMY).
• The retina contains three types of color receptor cells (or cones), since humans are trichromatic.

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.

Engineering

• A triangle is a polygon with three edges and three vertices. It is the most stable physical shape, which is why it is widely used in construction, engineering, and design.

Trivia

• There are only three consecutive odd prime numbers: [3, 5,7]. After that, it becomes impossible because every 3rd positive integer is composite since it is a multiple of 3.
• For the same reason, there are only three consecutive prime numbers that end with the same last digit and are separated by 10, they are [3,13,23].
• 3 is the only additive prime such that the sum of its digits is equal to 3. This is because all other numbers whose digits add up to a multiple of 3 are divisible by 3.
• 3 is the only prime number that when multiplied by 2 will give a perfect number. Only 6 is a perfect number, which when divided by 2 will give an odd number (3). So half of the remaining perfect numbers are also even, e.g. 28/2= 14, 496/2= 248, 8128/2= 4064. 3*2 = 6. The sum of the divisors without itself is (1+2+3=6) which is the same, so 6, (twice of 3) is perfect number.
  • For example, other prime numbers do not have this property, and for example, a multiple of 2 for other prime numbers will give a deficent number
  • 2*2 = 4 (1+2=3) 3 is less than 4.
  • 5*2 = 10 (1+2+5=8) 8 is less than 10.
  • 7*2 = 14 (1+2+7=10) 10 is less than 14.
  • 11*2 = 22 (1+2+11=14) 14 is less than 22.
  • 13*2 = 26 (1+2+13=16) 16 is less than 26.
• Only the prime powers 3 and the previous and first prime number 2 are called a cubes and squares, the remaining prime powers whose factor is not 2 and 3 do not create a spatial figure. This is because the world is three-dimensional, so the remaining prime powers: 5, 7, 11 etc. are abstract.

Prime Numbers 1-1,000