1. (programming required) Implement the Sieve of Eratosthenes in a programming language of your choice. Use your program to compute all primes up to 100,000. How many are there 2. (programming...

1. (programming required) Implement the Sieve of Eratosthenes in a programming language of your choice. Use your program to compute all primes up to 100,000. How many are there

2. (programming required) Earlier, we suggested another algorithm to compute all primes up to n := 100,000: for each i = 2, 3, . . . , n, test whether i is divisible by any integer between 2 and √ i. Implement this algorithm too, and compare their execution times. What happens for n := 500,000?