{"id":7560,"date":"2021-10-26T19:10:44","date_gmt":"2021-10-26T13:40:44","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7560"},"modified":"2022-01-16T17:08:38","modified_gmt":"2022-01-16T11:38:38","slug":"prime-numbers-in-math","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prime-numbers-in-math\/","title":{"rendered":"Prime Numbers in Math – Properties and Examples"},"content":{"rendered":"
Here you will learn what are prime numbers in math, its properties and method to check whether a number is prime or not.<\/p>\n
Let’s begin –<\/p>\n
A natural number larger than unity is a prime number if it does not have other divisors except for itself and unity.<\/p>\n
For example<\/strong><\/span> : 2, 3, 5, 7, 11 etc are all prime numbers.<\/p>\n Note<\/strong> : Unity (i.e. 1) is not a prime number.<\/p>\n 1). The lowest prime number is 2.<\/p>\n 2). 2 is the only even prime number.<\/p>\n 3). The lowest odd prime number is 3.<\/p>\n 4). The remainder when a prime number p \\(\\ge\\) 5 is divided by 6 is 1 or 5. However, if a number on being divided by 6 gives remainder of 1 or 5 the number need not be prime.<\/p>\n 5). The remainder of the division of the square of a prime number p \\(\\ge\\) 5 divided by 24 is 1.<\/p>\n 6). For prime numbers p > 3, \\(p^2\\) – 1 is divisible by 24.<\/p>\n 7). If a and b are two odd primes then \\(a^2 – b^2\\) is composite. Also, \\(a^2 + b^2\\) is composite.<\/p>\n 8). The remainder of the division of the square of a prime number p \\(\\ge\\) 5 divided by 12 is 1.<\/p>\n The prime numbers between 1 to 1oo are : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.<\/p>\n To check whether a number N is prime, adopt the following process.<\/p>\n 1). Take the square root of the number.<\/p>\n 2). Round of the square root to the immediately lower integer. Call this number z. For example if you have to check for 181, its square root will be 13… . Hence, the value of z, in this case will be 13.<\/p>\n 3). Check for the divisibility of the number N by all prime numbers below z. If there is no prime number below the value z which divides N then the number N will be prime.<\/p>\n<\/blockquote>\n Example<\/strong><\/span> : The value of \\(\\sqrt{239}\\) lies between 15 to 16. Hence take the value of z as 15.<\/p>\n Prime numbers less than 16 are 2, 3, 5, 7, 11 and 13, 239 is not divisible by any of these. Hence you can conclude that 239 is a prime number.<\/p>\n\n\nProperties of Prime Number<\/h3>\n
Prime numbers between 1 to 100<\/strong><\/h4>\n
Shortcut Method to Check Number is Prime or Not<\/h3>\n
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