Prime numbers are one of the most intriguing part of mathematics, as they follow no pattern and can be considered as building blocks of natural number series.
For high and mid school students, knowledge of prime numbers may be required in doing prime factorization to resolve larger composite numbers as product of primes or used in certain types of problems in Combinatorics in which a number needs to be expressed as a product of primes.
For prime factorization of large numbers, one needs to keep dividing them by prime numbers in a sequence, for which one needs to know some initial prime numbers. One can use this relation that all prime numbers after 5 are of the form 6n +/- 1 . This is a necessary but not sufficient condition. One needs to eliminate multiple os 5, 7, 11 etc from it. The following table gives some idea about it and rough pattern on prime numbers of two digits.