Definition of a Prime Number:

Those numbers that are not divisible by any number other than themselves and the number 1 are called Prime Numbers.

Mathematicians have not yet succeeded in finding out a definite method to identify the Prime Numbers from among the ocean of numbers.

However we are giving a few guidelines to identify the Prime Numbers within the set of numbers from 1 to1000.

1. 1 is neither a Prime Number nor a composite number.
2. Between 1 to 10 the following numbers are Prime Numbers: 2, 3, 5, and 7.
3. Prime Numbers from 11 onwards cannot end with the following numbers: 2, 4, 5, 6, 8, and zero because they are either divisible by 2 or 5.
4. All numbers, the total of whose digits, when reduced to a single digit are 3, 6, or 9 cannot be Prime Numbers.

If you remove the numbers mentioned in the steps 3 and 4 from the set of numbers from 11 to 1000, you will get a new set of numbers arranged in 33 rows with 8 numbers in each row, in all 264 numbers. The following table can be called as Srikrishnamangals Sieve.

Frm the above set of 264 numbers we have to sieve out those numbers, which are products of 2 or more Prime Numbers. The steps for the same are:

1. Multiply each of the numbers shown in the above table with 7 until the resultant products do not exceed 1000. Highlight these numbers by colouring or encircling.
2. Multiply each of the numbers in the table by 11 until the resultant products do not exceed 1000. Highlight these numbers also.
3. The same procedure of multiplication is to be followed in respect of 13, 17, 19, 23, 29 and 31, and the resultant products are to be highlighted.

In all you will get 100 such highlighted numbers, which are products of two or more Prime Numbers.

Sieve out all these 100 numbers from the above table by deleting them.

The remaining 164 numbers in the table are the Prime Numbers in the set of numbers between 11 and 1000. The table of these Prime Numbers is given below.

Adding the Prime Numbers 2, 3, 5 and 7 to the above set of 164 Prime Numbers, there are 168 Prime Numbers in all between the numbers 1 and 1000.

The purpose behind this endeavour is not to do any research in one of the greatest unsolved problems of Mathematics i.e. the distribution of Prime Numbers. Our only intention is to help the students of Mathematics to know these Prime Numbers and exclude them while searching for factors of a given number.

[Corrigendum: In the first edition, under the divisibility rules, we have said that all numbers the totals of whose alternate digits are equal, are divisible by 11. Though the statement is correct, it may also be noted that those numbers the totals of whose alternate digits differ by a number divisible by 11, are also themselves divisible by 11.]