Question

Find the range of first five prime numbers

Answer 1

Answer:

Highest value - Lowest value

numbers are 2,3,5,7,11

range - (11-2) = 9

The first 5 prime numbers are 2,3,5,7,11. Range = Highest value - The lowest value

Step-by-step explanation:

prime numbers

Those natural numbers greater than 1, which are not divisible by any natural number other than itself and 1, are called prime numbers.[1] Natural numbers greater than 1 which are not whole numbers are called composite numbers[ dead links]. The number of prime numbers is infinite, which was demonstrated by Euclid in 300 BC. 1 is not considered prime by definition. Since 1 is neither composite nor prime, 25 prime numbers are given below-

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, 101, 103

The importance of prime numbers is that the factor of any non-zero natural number can be expressed only by prime numbers and this factor is unique. This is called the fundamental theorem of arithmetic. I

The Rhind Papyrus attests to the knowledge of prime numbers in ancient Egypt. Detailed information on prime numbers is found in the book "Elements" by the ancient Greek mathematician Euclid (300 BC). The next detailed mention of a prime number comes from the 17th-century mathematician Pierre de Fermat (1601–1665). Fermat gave a formula by which prime numbers can be estimated. Fermat conjectured that any number that can be written in the form ( 2^2^n +1 ), where n is a natural number, is a prime number. Although this was true up to n=4, at n=5 the number which comes - (2^32 +1) is divisible by 641, so it is not a prime number. After this, the credit for the remarkable work on prime numbers goes to the German scientist and mathematician Johann Carl Friedrich Gauss (1777-1855).

There are many number series in mathematics, such as geometric series, parallel series, etc., with the help of whose formula any number of the series can be found, but no such series formula of prime numbers has been known because it is not a series. Does not follow a fixed pattern. This is still an unsolved problem in the field of mathematics.

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Answer 2

Answer:

The range of first five prime numbers is 9.

Step-by-step explanation:

Prime number is a number that can be divided exactly only by itself and 1. for example 7, 17 and 41.

The first five prime numbers are 2, 3, 5, 7, 11.

Now we will consider these numbers as a set which contains the first five prime numbers, so the range will be the difference of the highest and the lowest numbers in the set. The highest and lowest prime numbers which are subtracted are 11 and 2 respectively. So the range in mathematical form will be written as:

$Range = Highest term - Lowest term$

In the case of this question the highest term and the lowest term are seventh term and first term respectively.

⇒Range =5th term  -  1st term

On subtracting the number we get:

⇒Range= 9

∴ The range of the first five prime numbers is 9.

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