2

2
Basic Information
Cardinal Number	two
Ordinal Number	second
Roman Numeral	II
Greek Numeral	βʹ
Factorization	2
Standard Form	2 × 100
Different Representations
Binary Form	102
Ternary Form	23
Quaternary Form	24
Quinary Form	25
Senary Form	26
Septenary Form	27
Octal Form	28
Nonary Form	29
Undecimal Form	211
Duodecimal Form	212
Tridecimal Form	213
Quattuordecimal Form	214
Quindecimal Form	215
Hexadecimal Form	216
Septendecimal Form	217
Octodecimal Form	218
Novemdecimal Form	219
Vigesimal Form	220
Unvigesimal Form	221
Duovigesimal Form	222
Trevigesimal Form	223
Quattuorvigesimal Form	224
Quinvigesimal Form	225
Hexavigesimal Form	226
Septenvigesimal Form	227
Octovigesimal Form	228
Novemvigesimal Form	229
Trigesimal Form	230
Untrigesimal Form	231
Duotrigesimal Form	232
Tretrigesimal Form	233
Quattuortrigesimal Form	234
Quintrigesimal Form	235
Hexatrigesimal Form	236
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Current	2
Next	3

2 is the first prime number. It's the only even prime number, as all larger even numbers are divisible by 2, making them composite. Furthermore, it's the only prime number that's spelled without the letter "e", and only ordinal number that's spelled without the letter "t". The primorial of 2 is 2. Since this is the smallest prime number, This is the only case where the primorial is the same as the prime number because all primorials are divisible by more than one factor other than one.

Proofs

• — 2 is divisible by 1.

• — 2 is divisible by 2.

• Therefore it only has two factors.

Every even number is divisible by 2. Therefore, the only even prime is 2 because all larger even numbers will be divisible by at least three factors - itself, 2 and 1

Unique Properties

• 2 is only even prime number, and one of two numbers that does not have a last digit 1, 3, 7 or 9, the other exception being the number 5. Moreover, only 2 and 5 are untouchable prime numbers. Untouchable numbers are even (the exception is 5), and 2 is the only even prime number. So first two untouchable numbers, and all one-digit untouchable are prime, and the next untouchable numbers are 52, 88, 96 and 120 (so even and also composite numbers).
• Only the prime powers 2 and next prime number 3 are called a square and cube, 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.
• 2 (two) is the only prime number without an e in its name. This is because 2 is the only even prime number, and all odd numbers have at least one e in their name:
  • one
  • three
  • five
  • seven
  • nine
  • eleven
  • ,,,,,teen
    • -teen is a suffix, though it still has two e's, proving the aforementioned point.
• 2 (second) is the only prime number without an t in its ordinar. This is because 1 in ordinar is "first", and 3 in ordinar is "third", and all numbers with last digit 4,5,6,7,8,9,0 in ordinar end with "th", so only a number that has a last digit of 2 may not have a t in ordinary. As an interesting fact, the second number that does not have a t is much bigger and is 102 (one hundred and second), and the third number without t is 402 (four hundred and second).
  • first
  • third
  • fifth
  • seventh
  • ninth
  • eleventh
  • ,,,,,teenth
    • -teenth is a suffix, though it still has two t's, proving the aforementioned point.
• All even numbers are divisible by 2, including all even negative numbers (-2, -4, -6...) and 0.
• $2+2=2\times2=2^2$
• $\sum_{k=1}^\infty\frac{1}{k^2} \not= 2$ (this equals π^2/6 = 1.6449340668482264364724151666460251892189499012067984377355582293...)
• $\sum_{k=0}^\infty\frac{1}{2^k} = 2$

As an Exponent of Mersenne Number

$2^2-1$ is a formula for 3, which is a prime number. 3 is the first Mersenne prime, since $2^{1}-1=1$ and $2^{0}-1=-1$ are not prime.

Relationship with other numbers

The numbers before

No number less than 2 is a prime number.

• No negative number is a prime number since they are divisible by both negative and positive factors.
• 0 is not a prime number, because by definition, 0 has an infinite amount of divisors, without itself, so 0 is not a prime number, also it isn't a composite number because 0 is not divisible by itself.
• 1 is not a prime number. If we only consider the first prime criteria, 1 is prime since it is divisible by 1 and itself. However, if we also consider the second prime criteria, which is having exactly 2 divisors, 1 is not prime since it is only divisible by 1 divisor (1 and itself in one, instead of two separate divisors, e.g. Prime Number 2, with divisors 1 and 2, or Prime Number 3, with divisors 1 and 3.)
  • Negative divisors do not count.

The numbers after

• The next odd number, 3, is a prime number.
• 4 is the first composite number, with 3 factors, 1, 2 and itself (4).
• 5, the odd number following 3, is a prime number.
• 6 is the second composite numbers, first perfect number, and first with 4 factors, 1, 2, 3 and itself (6).
• 7 is the odd number following 5, is a prime number.
• 8 is the third composite number, and the first cube number 2³.

Usage

Science

• 2 is the atomic number of helium, meaning that there are two protons and electrons in a helium atom. There are also two neutrons in helium-4, the most common isotope of helium.
• There are two electrons in the first full electron shell of an atom.
• Group two elements are alkaline earth metals. They have a valency of 2.
• Deuterium, an isotope of hydrogen, has an atomic mass of two.

Technology

• Binary (or Base-2) is used in computing as on/off signals.

Sports

• In basketball, any shot not outside the three-point field goal is equal to two points, unless the player who threw the ball is fouled while attempting the shot.
• In Association football (soccer), the scoring of two goals by one individual in a single match is referred to as a brace.
• In American football, the scoring of two points is called a safety, which can be obtained by sacking the quarterback from the goal line to the 5 yard line. Sacking the quarterback makes the line of scrimmage 6 yards back, putting the line of scrimmage into the end zone. The defensive team gains two points.

Prime Numbers 1-1,000