Sure! Here's a Python script that should meet your requirements:

```python
def is_prime(n):
    if n <= 1:
        return False
    elif n <= 3:
        return True
    elif n % 2 == 0 or n % 3 == 0:
        return False
    i = 5
    while i * i <= n:
        if n % i == 0 or n % (i + 2) == 0:
            return False
        i += 6
    return True

def find_primes(start, end):
    primes = []
    for num in range(start, end + 1):
        if is_prime(num):
            primes.append(num)
    return primes

start = int(input("Enter the start of the range: "))
end = int(input("Enter the end of the range: "))
primes = find_primes(start, end)
print("Prime numbers between", start, "and", end, "are:")
print(primes)
```

This script defines two functions: `is_prime()` and `find_primes()`. `is_prime()` is a function that checks whether a number is prime or not using the efficient Miller-Rabin primality test algorithm. `find_primes()` is a function that takes in two numbers, `start` and `end`, and returns a list of prime numbers between `start` and `end`.

The script then prompts the user to input the start and end of the range of numbers they want to check for primes. It calls `find_primes()` with these inputs and prints out the resulting list of prime numbers.

I hope this script helps! Let me know if you have any questions.
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