Prime number/Citable Version: Difference between revisions
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A '''prime number''' is a whole number (i.e, one having no fractional or decimal part) that cannot be evenly [[divisor|divided]] by any numbers but <math>1</math> and itself. The first few prime numbers are <math>2</math>, <math>3</math>, <math>5</math>, <math>7</math>, <math>11</math>, <math>13</math>, and so on. With the exception of <math>2</math>, the first few numbers on this list are [[odd]] numbers, but not every odd number is prime. For example, <math>9 = 3\cdot3</math> and <math>15 = 3\cdot5</math>, so neither <math>9</math> nor <math>15</math> is prime. | A '''prime number''' is a whole number (i.e, one having no fractional or decimal part) that cannot be evenly [[divisor|divided]] by any numbers but <math>1</math> and itself. The first few prime numbers are <math>2</math>, <math>3</math>, <math>5</math>, <math>7</math>, <math>11</math>, <math>13</math>, and so on. With the exception of <math>2</math>, the first few numbers on this list are [[odd]] numbers, but not every odd number is prime. For example, <math>9 = 3\cdot3</math> and <math>15 = 3\cdot5</math>, so neither <math>9</math> nor <math>15</math> is prime. The study of prime numbers has a long history, going back to ancient times, and it remains an active part of [[number theory]] (a branch of [[mathematics]]) today. It is commonly believed that he study of prime numbers is an interesting, but not terribly useful, area of mathematical research. This, however, is a misundertanding. Fore example, it is now well known that understanding properties of prime numbers is essential to modern [[cryptography]], and to [[public key cipher]]s that are crucial to [[Internet]] commerce, [[wireless networks]], [[telemedicine]] and, of course [[military]] applications. But while it is commonly known that knowledge of prime numbers is important to cryptography, it is less well known that other [[computer]] [[algorithm]]s depen on properties of prime numbers. These algoritms allow computers to run faster, [[computer network]]s to carry more data with a greate degree of reliability, and are basic to the operation of many [[consumer electronics]] devices, such as [[television]] sets, [[DVD player]]s, [[global positioning system|GPS]] devices, and more. Life as we know it today would not be possible without an understanding of prime numbers. | ||
[[Category:Mathematics Workgroup]] | [[Category:Mathematics Workgroup]] | ||
[[category:CZ Live]] | [[category:CZ Live]] | ||
Revision as of 20:50, 4 April 2007
A prime number is a whole number (i.e, one having no fractional or decimal part) that cannot be evenly divided by any numbers but and itself. The first few prime numbers are , , , , , , and so on. With the exception of , the first few numbers on this list are odd numbers, but not every odd number is prime. For example, and , so neither nor is prime. The study of prime numbers has a long history, going back to ancient times, and it remains an active part of number theory (a branch of mathematics) today. It is commonly believed that he study of prime numbers is an interesting, but not terribly useful, area of mathematical research. This, however, is a misundertanding. Fore example, it is now well known that understanding properties of prime numbers is essential to modern cryptography, and to public key ciphers that are crucial to Internet commerce, wireless networks, telemedicine and, of course military applications. But while it is commonly known that knowledge of prime numbers is important to cryptography, it is less well known that other computer algorithms depen on properties of prime numbers. These algoritms allow computers to run faster, computer networks to carry more data with a greate degree of reliability, and are basic to the operation of many consumer electronics devices, such as television sets, DVD players, GPS devices, and more. Life as we know it today would not be possible without an understanding of prime numbers.
