Properties of prime numbers are helpful in identifying whether a number is prime or not. They are as follows:. Look at the list of prime numbers from 1 to As already discussed the natural number one is not a prime number because it has one factor so we will begin with number 2. Let's cross-check the any two above listed prime numbers by taking out the possible factors of the number.
For example:. We can see that the above numbers are having only two factors those are number 1 and the number self and no other possible factors are there, therefore they are prime numbers. Look at the chart below that shows prime numbers from 1 to Check out these interesting articles to know more about prime numbers from 1 to and their related topics. By finding the factors of a number we can easily identify prime numbers from 1 to If there are more than two factors then it's a composite number and not a prime number.
If there are only two factors that are number 1 and number itself then it's a prime number. And remaining even numbers can be easily divided by 2.
SO, 2 is the only even number which is a prime number. Is a prime numbers? What is the smallest factor of ? IS a perfect square? Is divisible by any number?
Is 91 divisible by any number? What does the number symbolize? What does mean? Eratosthenes took the example of a sieve to filter out the prime numbers from a list of natural numbers and drain out the composite numbers. Students can practice this method, by writing the positive integers from the numbers 1 to and circling the prime numbers, and putting a cross mark to all the composite numbers.
Some of the properties of prime numbers are:. Every number that is greater than 1 can be divided by at least one prime number. Every even positive integer greater than the number 2 can be expressed as the sum of two primes. Except for number 2, all other prime numbers are odd. In other words, we can say that two is the only even prime number.
Two prime numbers are coprime to each other. Prime Numbers. Composite Numbers. A prime number has only two factors. Pierre Dusart [ Dusart99 ] made these results stronger and showed. Dusart's article also gives better bounds getting even closer to the next term in the following well known asymptotic expansion for p n. The first terms of this asymptotic expansion were given by Cipolla [ Cipolla ] in Again Ribenboim95 and Riesel94 are excellent starting places to look up more information.
By the way, if you are interested in the n th prime for small n say less than 1,,, , then use the n th prime page. Let x be a positive integer. Below is a graph of the actual density for small values of x. Clearly Legendre's conjecture is equivalent to the prime number theorem, the constant 1. In the long run 1 is a better choice than Legendre's 1. Gauss was also studying prime tables and came up with a different estimate perhaps first considered in , communicated in a letter to Encke in and first published in Notice again that Gauss' conjecture is equivalent to the prime number theorem.
Let's compare these estimates:. A much better approximation than any of these is the Riemann function [ Ribenboim91 , Riesel94 ]. An easier to read but less elementary proof is in Hardy and Wright's text [ HW79 sect. The error term depended on what was known about the zero-free region of the Riemann zeta function within the critical strip.
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