How can we filter out numbers less than 2 in a number sequence to find prime numbers?

Answer 1

To filter out numbers less than 2 in a number sequence to find prime numbers, you can follow these steps:

1. Understand Prime Numbers: A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. Therefore, the smallest prime number is 2.

2. Create a Sequence: Begin with your number sequence which could be a list of numbers (e.g., [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]).

3. Filter Numbers: Remove any numbers that are less than 2, as they cannot be prime.

   For example, from the sequence [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], you would filter it to get [2, 3, 4, 5, 6, 7, 8, 9, 10].

4. Identify Prime Numbers: For each number in the filtered sequence, check if it is prime. To determine if a number \( n \) is prime, you can follow these steps:

   • Check for divisibility from 2 to the square root of \( n \).
   • If \( n \) is divisible by any of these numbers, it is not prime. If it is not, then it is prime.

5. Collect Results: Create a list of numbers that are identified as prime.

Example in Python

Here's how you can implement this in Python:

def is_prime(n):
    if n < 2:
        return False
    for i in range(2, int(n**0.5) + 1):
        if n % i == 0:
            return False
    return True

def filter_primes(sequence):
    # Filter out numbers less than 2
    filtered_sequence = [num for num in sequence if num >= 2]
    # Find and return prime numbers from the filtered sequence
    prime_numbers = [num for num in filtered_sequence if is_prime(num)]
    return prime_numbers

# Example usage
sequence = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
primes = filter_primes(sequence)
print(primes)  # Output: [2, 3, 5, 7]

Summary

By filtering out numbers below 2 and then checking for primality, you can effectively find all prime numbers in a given sequence.