Problem p01958 - Generation 1

Orig Description

Prime-Factor Prime
  A positive integer is called a "prime-factor prime" when the number of its prime factors is prime. For example, $12$ is a prime-factor prime because the number of prime factors of $12 = 2 \times 2 \times 3$ is $3$, which is prime. On the other hand, $210$ is not a prime-factor prime because the number of prime factors of $210 = 2 \times 3 \times 5 \times 7$ is $4$, which is a composite number.
In this problem, you are given an integer interval $[l, r]$. Your task is to write a program which counts the number of prime-factor prime numbers in the interval, i.e. the number of prime-factor prime numbers between $l$ and $r$, inclusive.
Input
  The input consists of a single test case formatted as follows.
$l$ $r$
A line contains two integers $l$ and $r$ ($1 \leq l \leq r \leq 10^9$), which presents an integer interval $[l, r]$. You can assume that $0 \leq r-l < 1,000,000$.
Output
Print the number of prime-factor prime numbers in $[l,r]$.
Sample Input 1
1 9
Output for Sample Input 1
4
Sample Input 2
10 20
Output for Sample Input 2
6
Sample Input 3
575 57577
Output for Sample Input 3
36172
Sample Input 4
180 180
Output for Sample Input 4
1
Sample Input 5
9900001 10000000
Output for Sample Input 5
60997
Sample Input 6
999000001 1000000000
Output for Sample Input 6
592955
In the first example, there are 4 prime-factor primes in $[l,r]$: $4,6,8,$ and $9$.

Extracted Specification

An integer \( l \) and an integer \( r \) (1 ≤ \( l \) ≤ \( r \) ≤ 10^9) with the constraint \( 0 \leq r - l < 1,000,000 \).

### Example Input:

```
1 9
```

### Function Signature:
Write a function f(l, r) that takes in the input. 
def f(l: int, r: int): 
    ''' 
    l: an integer 
    r: an integer
    '''

Test Case Generator

Sure! Let's build a test case generator for the "Prime-Factor Prime" problem. This generator will create random intervals `[l, r]` according to the constraints given in the problem statement.

Here's the Python code to generate such test cases:

```python
import random

def tcgen():
    # Generate l and r such that 1 ≤ l ≤ r ≤ 10^9 and 0 ≤ r - l < 1,000,000
    l = random.randint(1, 10**9 - 999999)  # Ensuring that r can go up to 10^9
    r = l + random.randint(0, 999999)
    
    return l, r

# Example usage
for _ in range(5):
    l, r = tcgen()
    print(l, r)
```

### Explanation:

1. **Generating `l`**: 
   - We use `random.randint(1, 10**9 - 999999)` to ensure that `l` is within the range `[1, 10^9 - 999999]`. This ensures that adding a number between `0` and `999999` to `l` will keep `r` within the limit of `10^9`.

2. **Generating `r`**: 
   - We set `r` as `l + random.randint(0, 999999)` to ensure that the difference `r - l` is always less than `1,000,000`.

3. **Output**: 
   - The generator returns a tuple `(l, r)` which represents the interval.

### Example usage:
The example usage part of the code generates and prints 5 random test cases.

Feel free to run the code to generate test cases for the "Prime-Factor Prime" problem!

Extract Arguments

def extract_arguments(fh):
    l, r = map(int, fh.readline().strip().split())
    return l, r