Question

What is the rule that describes the pattern of numbers: \[2,3,5,7,11,13,17,19,23,29\] ?

Answer 1

Hint: In this type of question students have to use knowledge of prime numbers. Prime number is a number that is divisible by itself and 1 only. In case of prime numbers we have to note that 2 is the only one prime number which is even and the rest all prime numbers are odd numbers. Also we must remember that 1 is neither prime nor composite number so that 2 is the smallest prime number.

Complete step-by-step answer:
Now, here we have given the pattern of numbers as follows:
\[\Rightarrow 2,3,5,7,11,13,17,19,23,29\]
If we observe each of the numbers then we can say that every number has only two factors, 1 and the number itself. We know that, if a number is divisible by itself and 1 only then it is called as a prime number. So in the above pattern all numbers are prime numbers. Also if we consider any two successive prime numbers from the above sequence then we can observe that all the integers present in between are composite numbers. Also 2 is the smallest prime number.
So we can say that the given pattern of numbers: \[2,3,5,7,11,13,17,19,23,29\] will describe the first ten prime numbers.

Note: In this type of question student may make mistake in identifying the pattern. Students have to take care about the number pattern. Also one can define the number pattern as prime numbers less than 30 or prime numbers from 1 to 30.