Prime Number Filter and Range Query

This problem requires implementing key functionalities related to prime numbers. You are to write a program that supports three operations: checking if a number is prime, filtering a list to contain only prime numbers, and listing all prime numbers within a specified range.

Functions to Implement:

• is_prime(n): Returns \(True\) if \(n\) is a prime number, otherwise \(False\).
• filter_primes(numbers): Given a list of integers, returns a new list containing only the prime numbers.
• range_primes(start, end): Returns a list of all prime numbers in the range \([start, end]\) (inclusive).

Your program must read input from stdin and output the results to stdout for each query.

inputFormat

The first line of input contains a single integer \(T\), denoting the number of queries.

Each of the following \(T\) lines represents a query in one of the following formats:

• is_prime n: Check whether \(n\) is a prime number.
• filter_primes k num1 num2 ... numk: Given \(k\) integers, output only the prime numbers among them.
• range_primes start end: Output all prime numbers in the inclusive range \([start, end]\).

outputFormat

For each query, output the result on a separate line:

• For is_prime: output \(True\) or \(False\) (case-sensitive).
• For filter_primes and range_primes: output the list of prime numbers separated by a single space. If no primes are found, output an empty line.

3
is_prime 17
filter_primes 5 2 4 6 7 11
range_primes 10 20

True
2 7 11
11 13 17 19