Prime numbers how many are there

Their method "is similar to the one described by Lagarias and Odlyzko, but uses the Weil explicit formula instead of complex curve integrals" see their e-mail announcing the result in July This value was later verified unconditionally by D.

Platt [ Platt ]. In May , J. Jost, and T. For example, x 2 is asymptotic to x 2 - x , but the difference between them, x , gets arbitrarily large as x goes to infinity. Let p n be the n th prime. It is easy to show that the prime number theorem is equivalent to the statement.

A better estimate is. 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.

Co-prime numbers are the numbers whose highest common factor is 1. For example, 2 and 3 are co-prime numbers. Co-prime numbers can be prime numbers too or non-prime numbers too. A number is called prime if it does not have any factors except 1 and itself.

So, it has 3 and 29 also as factors along with 1 and Hence it is a composite number. Thus, 87 is not a prime number. The pair of primes that differ by 2 are known as twin prime numbers. Twin prime numbers up to can be given as, 3, 5 , 5, 7 , 11, 13 , 17, 19 , 29, 31 , 41, 43 , 59, 61 , 71, Prime numbers are the numbers that have exactly two factors, that are, 1 and the number itself.

The smallest prime number is 2 and the smallest composite number is 4. Therefore, the HCF of smallest composite number and smallest prime number is 2.

There are total 25 prime numbers up to Following is the list of prime numbers up to - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and Learn Practice Download. Prime Numbers Up to Any whole number which is greater than 1 and it is divisible only by 1 and the number itself, is known as a prime number. Definition of Prime Numbers 2. How to find Prime Numbers Up to 3. List of Prime Numbers Up to 4. Solved Examples on Prime Numbers 1 to Example 1: Which of the given two numbers is a prime number, 13 or 15?

Solution: Given numbers are 13 and So number 15 has more than two factors. Do you know all the prime numbers from 1 to ? Did you check if each number is divisible by the smaller numbers? Then, you definitely invested a lot of time and effort. Eratosthenes was one of the greatest scientists, who lived a few decades after Euclid, designed a smart way to determine all the prime numbers up to a given number. This method is called the Sieve of Eratosthenes.

Suppose you have to find the prime numbers up to n, we will generate the list of all numbers from 2 to n. Similarly, assign the next value of p which is a prime number greater than 2. There are 25 prime numbers from 1 to The complete list of prime numbers from 1 to is given below:. Check out few more interesting articles related to prime numbers for better understanding.

There is a difference between prime numbers and co-prime numbers. Co-prime numbers are always considered in pairs, while a single number can be interpreted as a prime number. If a pair of numbers has no common factor apart from 1, then the numbers are called co-prime numbers.

Co-prime numbers can be prime or composite, the only criteria to be met is that the GCF of co-prime numbers is always 1. This formula will give you all the prime numbers greater than Let's substitute a few whole numbers and check. A prime number chart is a chart that shows the list of prime numbers in a systematic order.

Given below is the prime number chart from numbers 1 to that shows the list of odd prime numbers highlighted in yellow. The set of prime numbers between any two numbers can be found by following a pattern. The following figure shows a few prime numbers encircled and striking off all the numbers divisible by these prime numbers. You can follow this pattern until you reach the square root of the larger number, that is, The number 15 has more than two factors: 1, 3, 5, and Hence, it is a composite number.

On the other hand, 13 has just two factors: 1 and Hence, it is a prime number. Therefore, 13 is a prime number. The factors of 20 are 1, 2, 4, 5, 10, and Thus, 20 has more than two factors. Since the number of factors of 20 is more than two numbers, it is NOT a prime number 20 is a composite number.

To check whether is a prime number or a composite we need to identify its factors first. The factors of are 1, 11, , Thus, has more than two factors. Since the number of factors of is more than two numbers, it is NOT a prime number. Hence, is a composite number. Numbers having only two factors i.

A number greater than 1, with exactly two factors, 1 and itself, is defined as a prime number in mathematics. Here are some examples of prime numbers: 2, 3, 31, , , etc.

One of the easiest methods to find that a given number p, is a prime number, is to check the number of factors of the number p. If p has exactly two factors, 1 and p, then we say that p is a prime number. The factors of 2 are 1 and 2. Since 2 has exactly two factors, therefore it is a prime number.