Definition of Prime Numbers
Ok, I am starting to give lectures on some topics in Algebra (Prime Numbers and and its definition). These are preliminary lectures or tutorials in mathematics. Discussing these math concepts is very important to further studies in math. This is the reason why I will be publishing more tutorials like this before posting more articles on how to solve math word problems.
A prime number (or prime for short) is a natural number (from positive 1 to positive infinity which is usually symbolized by the capital letter “N” in most math books and other references) that can only be wholly divided by 1 and itself. For theoretical reasons, the number 1 is not considered a prime (we shall see why later on in this chapter). For example, 2 is a prime, 3 is prime, and 5 is prime, but 4 is not a prime because 4 divided by 2 equals 2 without a remainder.
The first 20 primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71. Primes are an endless source of fascination for mathematicians. Some of the problems concerning primes are so difficult that even decades of work by some of the most brilliant mathematicians have failed to solve them. One such problem is Goldbach’s conjecture, which states that all even numbers greater than 3 can be expressed as the sum of two primes.
Geometric meaning of primes
Let’s start with an example. Given 12 pieces of square floor tiles, can we assemble them into a rectangular shape in more than one way? Of course we can, this is due to the fact that
15 = 15 X 1 = 3 X 5
We do not distinguish between 3 X 5 and 5 X 3 because they are essentially equivalent arrangements (Commutative Property of Multiplication).
But what about the number 7? Can you arrange 7 square floor tiles into rectangular shapes in more than one way? The answer is no, because 7 is a prime number where the only factors are 1 and 7 (itself).
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