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Mathematics Dictionary
Dr. K. G. Shih
Prime Numbers
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Q01. Definition of prime numbers 

Definition

    1. An integer has only two factors, 1 and number itself.
    2. An integer can only be divisible by 1 and the number itself.

Examples

    1. Number 1 is a factor of any integers.
    2. Number 2 is also a prime number. It is the only prime number which is even.
    3. All Prime numbers are odd numbers.

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Q02. Twin prime numbers 

Defintion

     Two prime numbers have difference of 2.

Examples

     1. Prime numbers 3 and 5 are twin prime numbers
     2. Prime numbers 5 and 7 are twin prime numbers

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Q03. Sum of two prime numbers are even

Definition

     1. This is proposed by .... 
     2. But there is no proof.
     3. Except number 2

Examples

     1. Two prime number : 3 + 5 = 8
     2. Two prime number : 5 + 7 = 12

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Q04. Prime number pattern

     
     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

    55    56    57    58    59    60

    61    62    63    64    65    66

    67    68    69    70    71    72

    73    74    75    76    77    78

    79    80    81    82    83    84

    85    86    87    88    89    90

    91    92    93    94    95    96

    97    98    99   100   101   102

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Q05. Integers can be expressed as product of prime numbers

Example 1 : Exprees 16 as product of prime numbers

     16 = 2*8 
        = 2*2*4
        = 2*2*2*2
        = 2^4 (2^2 = 2 to power of 4)

Example 2 : Exprees 945 as product of prime numbers

    945 = 5*189 
        = 5*3*63
        = 5*3*3*21
        = 5*3*3*3*7 
        = (3^3)*5*7 (3^3 = 3 to power of 3)

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