Answer :
Let's break down the problem.
First, we need to find a two-digit prime number where the sum of its digits lies between 15 and 20. The only prime numbers in this range are 17, 19, 29, and 59.
Next, we need to find a prime number between 50 and 99 (two-digit prime number) whose product of digits is not more than this prime number.
Let's start by checking the primes:
- 59: Product of digits = 5 * 9 = 45 (Not more than 59)
- 17: Product of digits = 1 * 7 = 7 (Less than 17)
- 19: Product of digits = 1 * 9 = 9 (Less than 19)
- 29: Product of digits = 2 * 9 = 18 (Less than 29)
So, the only prime number that meets the criteria is 59. Its product of digits is 45, which is not more than 59, and the sum of its digits is 5 + 9 = 14, which falls between 15 and 20.
Therefore, the prime number you are referring to is 59.