A potential mathematical breakthrough suggests that prime numbers may have predictability

Consult any mathematician, and they will affirm the same fact: the prediction of prime numbers is impossible. It is undeniable in the field that these foundational components of mathematics—numbers that can only divide by one and themselves—are pseudorandom. Is it not?

Researchers from the City University of Hong Kong and North Carolina State University suggest that the answer may be negative. Way Kuo, a senior fellow at the Hong Kong Institute for Advanced Study at City University, stated that our team has developed a method to accurately and quickly predict the occurrence of prime numbers. The team has introduced a system called the “Periodic Table of Primes” (PTP), which the developer describes as a “truly revolutionary” advancement in the field of number theory.

The working paper, which is currently awaiting peer review, asserts that the PTP offers a platform that enhances the clarity and simplicity of studying prime numbers.

The article highlights three significant contributions: the Formula of Primes, the Periodic Table of Primes, and the Counting Functions for Primes and Twin Primes. These results answer important questions for the academic community, like what the next prime number will be, how to factor an integer, show the fundamental theorem of arithmetic, guess the total number of prime numbers and twin primes, or find the biggest difference between two prime numbers that are close together in a certain range.

If none of that is familiar to you, then believe us: it is essentially a compilation of the most noteworthy concepts from number theory. These questions have been pondered for centuries, if not longer, and are connected to some of the most renowned unresolved mathematical problems.

However, even if you do not possess extensive knowledge of mathematics, this discovery would still be a significant advancement. Prime numbers play a fundamental role in various aspects of our lives, extending beyond a mere curiosity in arithmetic. Ittay Weiss, a teaching fellow in the Department of Mathematics at the University of Portsmouth, highlighted in a 2018 article for The Conversation that the RSA encryption system is a highly utilized application of prime numbers in computing. The system enables the secure transfer of information, such as credit card numbers, over the internet.

“Prime numbers of significant magnitude are also utilized prominently in other cryptographic systems,” Weiss added. The inherent value of prime numbers lies in their unpredictability, which is crucial for many applications. For instance, RSA encryption relies on the challenge of prime factorization. Therefore, if a method to predict prime numbers were discovered, it could significantly simplify the process of encrypting and decrypting information.

Undoubtedly, the extent to which this breakthrough is truly revolutionary remains to be determined. The paper remains a preprint, indicating that it has not yet undergone peer review. It is worth mentioning that none of the three authors are professional mathematicians. However, it is worth noting that achieving such results is not impossible for individuals who are not members of the math club. For instance, Banach, an engineer, and Nightingale, a nurse, were able to accomplish remarkable feats. Nevertheless, we are referring to problems that have perplexed the most brilliant mathematicians for thousands of years. Undeniably, the current situation is demanding and challenging.

The research is available on the SSRN preprint repository.