Identify these prime numbers from the clues.
(a) it is less than 30.
the sum of its digits is 8.
(b) it is between 30 and 60.
the sum of its digits is 10.

The prime number that is less than 30 and its digits sums to 8 is 17.

The prime number that lies between 30 and 60 and its digits sum to 10 is 37.

Explanation:

Prime number:

A whole number that is greater than 1 and having factors as 1 and itself is called as prime number.

(a)The prime numbers that are less 30 are

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Here 17 is the only prime number where the sum of their digits is 8

1+7=8

Hence 17 is the prime number that is lesser than 30 whose digit sum is 8.

(b)The prime number that lies between 30 and 60 are

31,37,41,43, 47, 53, 59

Here 37 is the only prime number where the sum of their digits is 10

3+7=10

Hence  37 is the only prime that lies in between 30 and 60 and has the digit sum as 10.