Final answer:
To use the Sieve of Erastosthenes to find all prime numbers in the interval (50,100), create a list of numbers, mark the multiples of each number as composite numbers, and find the unmarked numbers.
Step-by-step explanation:
To use the Sieve of Erastosthenes to find all prime numbers in the interval (50,100), you start by creating a list of numbers from 2 to 100.
Then, you mark the multiples of each number starting from 2 as composite numbers. For example, for the number 2, you mark its multiples 4, 6, 8, etc. as composite numbers.
Repeat this process for each unmarked number until you reach the square root of the largest number in the interval. Finally, the numbers that remain unmarked are the prime numbers in the interval (50,100). In this case, the prime numbers are 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.