Prime Numbers Example

The Prime numbers are the numbers that can only be divided exactly between unity and the number itself.

Prime numbers are a part of the positive whole numbers which have the special feature that you can only make exact divisions with them, when the number is divided by itself (resulting in 1) and by unity, resulting in the same number.

Characteristics of prime numbers:

Prime numbers are odd, with the exception of the number 2, which is the only even.

• The number 1 is not a prime number, it is the unit.
• There is no formula for calculating prime numbers.
• Numbers that are not prime are called composite numbers.
• The sum of two prime numbers other than 2, results in a composite number.
• Subtracting two prime numbers other than 2 gives a composite number.
• The number 2 can be added or subtracted with other prime numbers, resulting in some prime numbers and some composite numbers.
• Multiplying two prime numbers results in composite numbers.
• All whole numbers are formed by the multiplication of one or more prime numbers.

With prime numbers, all mathematical operations can be performed, since they are part of the natural numbers. In the results we can obtain non-prime primes, according to the rules explained above.

An important use of prime numbers is factoring. Factoring is the characteristic of numbers and the mathematical principle that says that everything whole number greater than 1, can be expressed as the product or multiplication of one or more numbers cousins. Each of the numbers that make it up is called a prime factor. When a number has the same prime factor several times, it is expressed as a power.

Thus, for example, the number 2 has as its prime factor the same number 2.

The number 6 is composed of the prime factors 2 and 3 (2X3 = 6)

The number 12 is composed of the prime factors 2, 2 and 3 can also be written as 2² and 3 (2X2X3 = 12; 2²X3 = 12) 

Examples of prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97…

Sums of prime numbers:

2 + 3 = 5 (Prime number)
5 + 2 = 7 (prime number)
7 + 2 = 9 (composite number)
13 + 5 = 18 (composite number)
5 + 7 = 12 (composite number)

Subtraction of prime numbers:

13–5 = 8 (composite numbers)
13–2 = 11 (prime number)
23–2 = 21 (composite number)
37–7 = 30 (composite number)
43–2 = 41 (prime number)

Prime Number Multiplications:

2X3 = 6
11X3 = 33
29X5 = 145
17X7 = 119
13X11 = 143

Division of prime numbers:

11/11 = 1
11/1 = 11
89/89 = 1
89/1 = 89
41/41 = 1
41/1 = 41

Examples of factoring in prime numbers:

Factor 121:

121 | 11
11 | 11
0

The prime factors of 121 are 11 and 11, or 11²

Factor 122:

122 | 2
61 | 61
0

The prime factors of 122 are 2 and 61

Factor 123:

123 | 3
41 | 41
0

The prime factors of 123 are 3 and 41

Factor 124:

124 | 2
62 | 2
31 | 31
0

The prime factors of 124 are 2, 2, and 31, or 2² and 31

Factor 125:

125 | 5
25 | 5
5 | 5
0

The prime factors of 125 are 5, 5, and 5, or 5³