Prime And Composite Numbers

Prime Numbers

A prime number is a whole number greater than 1 that is divisible only by 1 and itself (the remainder is 0). For example the first ten primes as: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. For example, the only numbers that divide into 5 are 1, and 5. Some interesting facts about prime numbers:

The only even prime is 2. All other even numbers are divisible by 2 and therefore are not prime.

There are only two primes that are next to each other in the list of whole numbers. These are 2, and 3.

Two successive odd numbers that are both prime are said to be prime pairs. For example 3 and 5, 5 and 7, and 13 and 15 are all prime pairs.

There is no largest whole number. The whole numbers keep getting larger without end. Is there a largest prime? (The answer is no). Are there a largest prime pair? (Interesting question)

If you construct a table of primes, all the primes above 6 are either in column 1 or column 5.

A Beginning List Of Primes

Column 1	Column 2	Column 3	Column 4	Column 5	Column 6
1	2	3	4	5	6
7	8	9	10	11	12
13	14	15	16	17	18
19	20	21	22	23	24
25	26	27	28	29	30
31	32	33	34	35	36
37	38	39	40	41	42
43	44	45	46	47	48
49	50	51	52	53	54

• The prime numbers are in red.

• The composite numbers are in black.

• Except for the first row of numbers all primes lie either in column 1 or column 5.

• The prime number 2 eliminates all possible primes in columns 2, 4, and 6.The prime number 3 eliminates all possible primes in column 3.

• No matter how large you make this list of numbers the primes will always fall either in column 1 or in column 5.

Composite Numbers

A composite number is a number that has more divisors then just 1 and itself. For example the number 6 has 4 divisors, namely: 1, 2, 3, and 6. We call these factors of the number 6. The first 10 composite numbers greater than 1 are: 4, 6, 8, 9, 10, 12, 14, 15, 16, and 18. Some interesting facts about composite numbers:

All even numbers are composite except for the number 2.

A composite number can be written as a product of primes. Examples: 6 = 3 * 3, 8 = 2 * 2 * 2, and 10 = 2 * 5.

The factors of a composite number are all those numbers that divide into the composite number, including itself. For example: 6 has the factors 1, 2, 3, and 6. 8 has the factors: 1, 2, 4, and 8.

Here is an interesting problem from number theory. The proper factors are all those factors of a number that are less then that number. For example: the proper factors of 6 are 1, 2, and 3. The proper factors of 8 are 1, 2, and 4. Notice that the proper factors of 6 when added together equal 6 (1 + 2 + 3 = 6). 6 is said to be a perfect number. Can you find another perfect number? (There is another one that is less then 30.) Between 1 and 10,000 there are only four numbers that are perfect.