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2 is the first prime number in the base ten numbering system. It is said to be the only even prime number, as all other even numbers are divisible by 2, making them composite.

Proofs

• — 2 can be divided by 1.
• — 2 can be divided by 2.
• Therefore it only has two factors.

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

Unique Properties

• 2 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 an e in their name.
• A number is called even if and only if it is divisible by 2.
• $2+2=2\times2=2^2$
• $\sum_{k=1}^\infty\frac{1}{k^2} \not= 2$
• $\sum_{k=0}^\infty\frac{1}{2^k} = 2$

As an Exponent of Mersenne Number

22 - 1, which is the number 3, is a prime number. It is the 1st Mersenne Prime.

Relationship with other numbers

The numbers before

• There are no prime numbers before 2.
• 1, the number before 2, is not a prime number, because it only has 1 factor; itself.

The numbers after

• The next odd number, 3, is a prime number.
• 4 is the first composite number.
• 5, the odd number following 3, is a prime number.

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

• 2 is the resin identification code used in recycling to identify high-density polyethylene.

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, the scoring of two goals by one individual in a single match is referred to as a brace.
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