------
## 最终结论
```python
def intersection(interval1, interval2):
    # Calculate the start and end of the intersection
    start = max(interval1[0], interval2[0])
    end = min(interval1[1], interval2[1])
    
    # Check if there is an intersection
    if start > end:
        return "NO"
    
    # Calculate the length of the intersection
    length = end - start + 1
    
    # Function to check if a number is prime
    def is_prime(n):
        if n <= 1:
            return False
        for i in range(2, int(n**0.5) + 1):
            if n % i == 0:
                return False
        return True
    
    # Check if the length is prime
    if is_prime(length):
        return "YES"
    else:
        return "NO"
```