Title: Limitations of Prime Number Search Algorithms.

 Title: Limitations of Prime Number Search Algorithms.

Why Does the 'Sieve of Eratosthenes' Stop at Billions of Calculations?

In modern computing systems, the efficiency of an algorithm is directly linked to the 'occupancy time' of system resources, going beyond mere execution time. A recent comparative test of prime number search algorithms (Standard Sieve vs. Sky Butterfly) revealed an interesting physical threshold.

 

 

1. Test Environment and Data Summary

• Measurement Intervals: 100,000, 1,000,000, 10,000,000,000 (Unit: sec)

• Notable Point: It was confirmed that as the interval increases, the performance gap between the two algorithms does not increase simply linearly, and the pattern of system resource occupancy changes completely after a certain interval.

 

 

Analysis of system bottlenecks at multi-billion units

The reason existing algorithms experience buffering (row) in billions of tests is because the "locality of the reference" of the data is destroyed.

 

 

• Memory Overhead: Standard algorithms cause memory swapping during the process of declaring and marking the entire array. This results in an extremely slow state where the CPU cannot utilize cache memory and reads data from the hard disk.

 

• Advantage of Pattern Filtering: The Sky Butterfly algorithm does not generate an entire array but adopts a structure that 'filters' prime candidate groups in real-time. This maintains a constant memory usage and provides a foundation for the system to continue computation without getting stuck in a hang.

 

 

3. Why is 'Absolute Time' More Important Than 'Multiplier'?

Many of you may notice that the magnification drops slightly after 100 million (6.8x → 4.9x). However, what you should focus on is the 'absolute amount of time saved.'

 

When scaled to units of 1 billion or more, standard algorithms experience 'non-linear degradation,' where the system freezes due to memory limits or slows down exponentially.

 

• On the other hand, Sky Butterfly maintains the 'linearity' of computational efficiency through its filtering structure. This means that as big data computing approaches, it creates an overwhelming gap that is incomparable to existing algorithms.

 

4. Conclusion: 'Green Computing' Created by Algorithm Efficiency

 

Reducing computation time is not merely about increasing processing speed, but is a 'practical eco-friendly technology' that immediately reduces the thermodynamic load on servers.

Switching from existing algorithms that cause buffering in billions of operations to algorithms that maximize resource efficiency will be the key to simultaneously solving data center operating costs and carbon footprints.