The algorithm described is known as the "Sieve of Eratosthenes." It is a simple and efficient algorithm used to find all prime numbers up to a specified integer value.
Here is a Python implementation of the Sieve of Eratosthenes algorithm:

```python
def sieve_of_eratosthenes(x):
    primes = []
    sieve = [True] * (x+1)
    sieve[0] = sieve[1] = False

    for i in range(2, int(x**0.5) + 1):
        if sieve[i]:
            primes.append(i)
            for j in range(i*i, x+1, i):
                sieve[j] = False

    for i in range(int(x**0.5)+1, x+1):
        if sieve[i]:
            primes.append(i)

    return primes

x = int(input("Enter a number x: "))
result = sieve_of_eratosthenes(x)
print(f"Prime numbers up to {x}:")
print(result)
```

You can run this code by inputting a value for x, and it will generate all prime numbers up to x as per the Sieve of Eratosthenes algorithm.