# FACT0RN Blockchain: Integer Factorization as Proof-of-Work (PoW)

*Tl;dr: This report updates on what **FACT0RN Blockchain**, a **Coinbase Crypto Community Fund** grant recipient, has been engaged on to switch PoW hashing by work that’s of curiosity to the personal sector in addition to to the tutorial group. Code for the FACT0RN Blockchain, which launched April 20, 2022, will be discovered **here** and the whitepaper will be discovered **here**.*

*By **Escanor Liones** (**Github*)

Proof-of-work (PoW) is the unique scheme to safe blockchain know-how launched in 2009 by Satoshi Nakamoto by means of the Bitcoin whitepaper. An analysis performed in late 2021 by the New York Times on the electrical energy utilization of the Bitcoin community indicated that the bottom electrical energy consumption estimate was on par with the overall electrical energy consumption of Washington State for a yr — and greater than 7 occasions as a lot as Google’s international operations.

Just this month, Forbes reported on a invoice that’s within the works in New York State, in addition to leaked European Union Documents, that sign to ‘A De Facto Ban` on proof-of-work mining in general, for Bitcoin and otherwise. It is worth noting that by and large PoW blockchains are based on some form of hashing — a mathematical function that is easy to compute forward and hard to reverse given an output.

There is a blockchain that uses finding prime constellations as its proof of work, and yet another searches for chains of prime numbers known as Cuningham Chains as its PoW. Vitalik Buterin published an article on July 7, 2013 on Bitcoin Magazine about the latter titled *“Primecoin: The Cryptocurrency Whose Mining is Actually Useful*” where he observed that “One of the disadvantages of Bitcoin that its proponents often gloss over is the fact that its mining algorithm has little real-world value. ”

The author of the PrimeCoin whitepaper in 2013 stated: “I would expect proof-of-work in cryptocurrency to gradually transition toward energy-multiuse, that is, providing both security and scientific computing values.” I would extend this to include commercial value in addition to security and scientific computing value.

**Beyond Bitcoin**

The digital security of banks, 500 Fortune companies, governments and many IoT devices depend on RSA — a cryptographic system whose security is provided by the difficulty of factoring integers into their prime factors, and in particular, the difficulty of factoring integers that only have two prime factors where both have exactly the same size in number of digits. These numbers are called strong semiprimes, and factoring them is the RSA problem.

It seems to me, after speaking with mathematicians, cryptographers, and random users on the internet, the reason a blockchain based on the RSA factoring problem has not been created until now is because no one could figure out how the blockchain could generate strong semiprimes for miners to factor without first knowing what the prime factors were.

My solution to this problem is simple: instead of generating strong semiprimes without knowing their factors a priori — which no one can figure out how to do — create conditions under which miners can find these strong semiprimes by way of factoring and reward them for finding them. In the process, tie the blockheader data to this process to secure the blockchain.

The essence of PoW is as follows: generate a random number by hashing the data in the block header of the block to be validated, give miners a range around this generated integer, and allow miners to factor all these integers. If they find a strong semiprime reward them accordingly. If they do not find a strong semiprime they can change the nonce and try again. The miners can generate as many random numbers as they want using nonces, but the search range allowed will always be about the same.

**Who cares about integer factorization?**

The RSA Challenge, created in 1991 by RSA Labs, has rewarded tens of thousands of dollars for factoring ever bigger integers into their prime factors. The largest such award was given to Jens Frenke in 2005 for factoring RSA-640 in the amount of $20,000 dollars.

As the Springer Encyclopedia of Cryptography and Security notes, “Starting in 1991, RSA Data Security offered a set of ‘challenges’ meant to measure the issue of integer factoring. The challenges consisted of an inventory of 41 *RSA Numbers*, every the product of two primes of roughly equal size, and one other, bigger record of *Partition Numbers* generated in line with a recurrence.”

In addition to the curiosity from personal trade there are greater than a dozen lively tutorial communities that issue integers as a pastime within the hopes of advancing our information of mathematical principle in numerous areas. The Cunningham Project has been factoring integers to this finish since 1925, sure 1925. The National Science Foundation within the United States funds this venture, partially, by means of XSEDE sources offered by the Texas Advanced Computing Center, the San Diego Supercomputer Center, the National Center for Supercomputing Applications, and Purdue University underneath grant quantity TG-DMS100027.

The mersenne prime search venture has been factoring within the quest to seek out ever greater primes for the reason that mid 90’s. There is a factoring venture for Aliquot Sequences, Brilliant Numbers, and the record goes on and on. The factoring curiosity within the tutorial group can’t be understated.

**The Future of PoW**

The concern at massive with the vitality consumption of PoW mining for blockchain know-how shouldn’t be in regards to the vitality utilization, however somewhat about the truth that the work for which the vitality is used improves no different a part of society or human endeavor in methods mere mortals can level to.

Increasingly, the areas of human endeavor that may profit from computation basically solely proceed to develop. The demand for computation can clearly be seen by the success of cloud computing giants like Amazon Web Services (AWS), Google Cloud, Azure by Microsoft, and a number of other different cloud companies which can be thriving at present. There aren’t any main issues in regards to the vitality consumption of those enterprises as a result of the work they do goes to assist small enterprise, hospitals, banks, universities, legislation corporations, finance establishments, and each type of group you may think about that have to compute to supply higher companies to serve society at massive.

The challenge shouldn’t be PoW mining, however as an alternative that till now the work in PoW has not gone to profit some other enterprise however the mining itself. FACT0RN is the primary PoW blockchain that seeks to drastically change this case by changing hashing by work that’s of curiosity to the personal sector in addition to to the tutorial communities and whose success will propel important funding for universities and mathematical analysis in normal.

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*Coinbase is formally searching for purposes for our 2022 developer grants centered on blockchain builders who contribute on to a blockchain codebase, or researchers producing whitepapers. Learn extra in regards to the **call for applications here**.*

FACT0RN Blockchain: Integer Factorization as Proof-of-Work (PoW) was initially revealed in The Coinbase Blog on Medium, the place individuals are persevering with the dialog by highlighting and responding to this story.