Question

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:

```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.