The correct answer is (b) 25.
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number.
The first 25 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, and 83.
To find the number of prime numbers between 1 and 100, we can use a sieve. A sieve is a way of listing all the prime numbers up to a certain number. To make a sieve, we start with a list of all the natural numbers from 2 to 100. Then, we cross out all the multiples of 2, starting with 2 itself. Then, we cross out all the multiples of 3, starting with 3 itself. We continue this process, crossing out all the multiples of each prime number as we encounter them. When we are finished, the remaining numbers are all the prime numbers between 1 and 100.
In this case, the sieve would look like this:
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
As you can see, there are 25 prime numbers between 1 and 100.