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Firstly, what is a prime number? Simply stated, a whole number that is only divisible by 1 or the number itself is called a prime number. It is greater than one and has only two factors. All prime numbers are odd numbers except 2. It is the only even prime number. Any number that has more than two factors is a composite number.<\/p>\n
Let\u2019s see a few examples.
For example, 2 is a prime number. The only two numbers it is divisible by are 1 and 2 or simply it only has two factors and can be written as (2 x 1) or (1 x 2).
3 is also a prime number. The number 3 can be factorized in one possible way which is (3 x 1) or (1 x 3).<\/p>\n
The 15 prime numbers from 1 to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.<\/p>\n
As you can see, all these numbers are either divisible by 1 or the number itself.<\/p>\n
Fact:<\/strong> 2 is the only even prime (non-composite) number which is even. It is so because all other even numbers are divisible by 2. All the other prime numbers, except 2, are odd.<\/p>\n <\/p>\n The answer to this question is <\/span>NO<\/i><\/b>. By definition, prime numbers have two factors, one is the number 1 and the other one is the number itself but the only factor for 1 is, well the number 1 itself.\u00a0<\/span><\/p>\n Generally, the concept of prime numbers is only limited to positive integers greater than 1. By definition, <\/span>prime numbers are positive<\/i><\/b>. The simple reasoning is that a prime number when taken with a negative sign has more than 2 factors.<\/span><\/p>\n For example, we know that 5 is a prime number but if we take -5 then it can be factorized and written as (-5 x 1) and (5 x -1) which would give 4 factors namely -5, 5, -1 and 1.\u00a0<\/span><\/p>\n <\/span><\/p>\n There are infinitely many prime numbers<\/i><\/b>. It simply means that the sequence of the prime numbers 2, 3, 5, 7, \u2026.. never ends. This is called Euclid\u2019s Theorem. The proof shows that any finite list of prime numbers is not complete.\u00a0<\/span><\/p>\n What are twin prime numbers?<\/b><\/p>\n The consecutive prime numbers that have the difference of 2 are called twin prime numbers. For example:<\/span><\/p>\n <\/span><\/p>\n A pair of numbers that have only 1 common factor are called co-prime numbers. Co-prime numbers are not necessarily prime numbers. A set of co-prime numbers can have a composite number or both the numbers can be composite as well. For example, 3 and 16 are co-primes because they have only one common factor which is the number 1. Also, note that here 16 is a composite number.<\/span><\/p>\n [\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][et_pb_text admin_label=”Related Concepts [\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” hover_enabled=”0″ locked=”off” global_colors_info=”{}” sticky_enabled=”0″]<\/p>\nIs 1 considered a prime number?<\/b><\/h2>\n
Do we have negative prime numbers as well?<\/b><\/h2>\n
So, how many prime numbers are there exactly?<\/b><\/b><\/h2>\n
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What are co-prime numbers?<\/b><\/h2>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nRelated Concepts<\/h1>\n