Given a number n, we need to find the product of all prime numbers between 1 to n.
Input: 5 Output: 30 Explanation: product of prime numbers between 1 to 5 is 2 * 3 * 5 = 30 Input : 7 Output : 210
Using Sieve of Eratosthenes to find all prime numbers from 1 to n then compute the product.
Following is the algorithm to find all the prime numbers less than or equal to a given integer n by Eratosthenes’ method:
- Create a list of consecutive integers from 2 to n: (2, 3, 4, …, n).
- Initially, let p equal 2, the first prime number.
- Starting from p, count up in increments of p and mark each of these numbers greater than p itself in the list. These numbers will be 2p, 3p, 4p, etc.; note that some of them may have already been marked.
- Find the first number greater than p in the list that is not marked. If there was no such number, stop. Otherwise, let p now equal this number (which is the next prime), and repeat from step 3.
When the algorithm terminates, all the numbers in the list that are not marked are prime and using a loop we compute the product of prime numbers.
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