Ethereum: Intrinsically useful proof-of-work through Mersenne or Fermat number factorization. Could this be possible? [closed]

Ethereum: A Possible Proof-of-Work System Using Non-Cryptographic Factors

The concept of proof-of-work (PoW) has been around for centuries, and its evolution into cryptocurrencies like Bitcoin has led to various proposals and experiments. One idea that has attracted attention is the use of non-cryptographic factors as a difficulty level in PoW systems. This approach is often referred to as “intrinsically useful” proof-of-work.

In this article, we will explore why such a system might be viable and discuss its potential applications.

What is Mersenne or Fermat Number Factorization?

Mersenne numbers are mathematical constants of the form \(2^k – 1\), where k is an integer. Fermat numbers are mathematical constants of the form \(F_k = 2^{2^k} + 1\). These numbers have been widely studied in mathematics and computer science, particularly for their potential applications in cryptography.

Why use Mersenne or Fermat numbers?

Using Mersenne or Fermat numbers as a difficulty level in PoW systems offers several advantages:

• Off-net value: As mentioned above, these numbers have significant properties that make them difficult to factor. This could be useful if we wanted to create a cryptocurrency that relies on non-cryptographic factors for its proof of work.

• Distributive nature: Mersenne and Fermat numbers have properties that can make their factoring difficulty grow exponentially with the number of rounds (k). This means that the difficulty level would increase rapidly, making it harder to solve.

• Scalability: Using these numbers could potentially lead to a more scalable PoW system, as the difficulty of factoring them increases faster than traditional PoW systems.

Can Ethereum use Mersenne or Fermat numbers?

While we have discussed the potential applications of using non-cryptographic factors in PoW systems, it is essential to note that Ethereum is built on a proof-of-stake (PoS) consensus algorithm. This means that the underlying technology and architecture are not directly compatible with this approach.

However, if Ethereum were to adopt a proof-of-work system based on Mersenne or Fermat numbers, it would require significant modifications to the Ethereum core. The team behind Ethereum, known as the Ethereum Foundation, has explored several alternatives to PoW systems in their proposals.

Potential challenges and limitations

While using non-cryptographic factors in PoW systems may offer some advantages, there are also potential challenges and limitations to consider:

• Mathematical complexity: Developing algorithms that can efficiently factor Mersenne or Fermat numbers would require significant mathematical advancements.

• Scalability and performance: The difficulty level of using these numbers could lead to slower transaction processing times and lower scalability, making them less suitable for high-traffic applications.

In conclusion, while using Mersenne or Fermat numbers as a proof-of-work system on Ethereum is theoretically feasible, there are significant challenges and limitations that must be considered. It is essential to carefully evaluate the potential benefits versus the drawbacks before considering such an approach.