![]() Less well-known is that other computer algorithms also depend on properties of prime numbers. Understanding properties of prime numbers and their generalizations is essential to modern cryptography - in particular to public key ciphers that are crucial to Internet commerce, wireless networks, and military applications. Although the study of prime numbers used to be an interesting but not terribly useful area of mathematical research, today it has important applications. The study of prime numbers has a long history, going back to ancient times, and it remains an active part of number theory today. ![]() ![]() For example, and so neither 9 nor 15 is prime. With the exception of 2, all prime numbers are odd numbers, but not every odd number is prime. ![]() as, except for the trivial factorizations that all numbers possess. The first few prime numbers are 2, 3, 5, 7, 11, 13, and 17.Ī prime number p cannot be expressed as the product of two numbers a and b, i.e. There is no way to form a full rectangle more than one square wide with 11 squares, so 11 is a prime number.Ī prime number is a whole number greater than 1 that can be evenly divided by only two different positive whole numbers, namely 1 and itself. 12 squares can be arranged into a rectangle with sides of length 3 and 4, so 12 is not a prime number. The prime number 11 illustrated with square tiles.
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