Prime numbers
limited short-term tangible benefits, the advancements made in number theory and computing justify the employed resources.
The search for ever larger prime numbers clearly sits between practical application and pure mathematical curiosity. The main issue, however, lies in the vast funding and use of resources to find numbers that simply have no current use in encryption, error detection or any other relevant applications. Not only is this use of energy expensive to fund, but it also raises environmental concerns due to the large scale of these searches, which can make it difficult to justify. The main argument for the continuation of the searches is that the benefits are far larger than just the found prime numbers themselves, with the advances in computing techniques and algorithms giving huge assistance to future engineering and scientific enquiries. Projects such as GIMPS also show the benefit of global collaboration and how this can lead to increased efficiency and ultimately reaching an objective faster. There are also upcoming issues, with the development of quantum computing leading to new threats to the current cryptographic systems. This in itself could create demand for an increased value of extremely large prime numbers to create further security. In conclusion, the search for ever-larger primes poses both economical and environmental concerns, along with a huge opportunity cost of the resources expended. However, I believe these searches have pushed forward the limitations of number theory and computation and will continue to do so. The argument for it purely being a case of mathematical curiosity may hold relevance in the short term, but the history of mathematics has proved to us that concepts and ideas often find use and significance many years after creation and also, in themselves, can unlock and trigger wider related uses and applications in related areas. The search has led to many developments in computing, so even if these extremely large prime numbers never find any practical use, the search will still have benefited the scientific community. Abandoning the search would be halting technological and mathematical advancements and therefore cannot be supported. Ultimately, my view is that this search should be continued, but the focus must remain on improving technology and increasing our understanding of mathematics. While environmental and economic factors should remain a key consideration, my sense is that these factors are outweighed on the whole by the wider benefits themselves. Bibliography Murtagh, J. New Prime Number, 41 Million Digits Long, Breaks Math Records . https://www.scientificamerican.com/article/new-prime-number-41-million-digits-long-breaks-math- records/. Consulted: 13/08/25 Lee, S. The Power of Prime Numbers: A Guide to Algorithmic Number Theory. https://www.numberanalytics.com/blog/power-prime-numbers-guide-algorithmic-number-theory. Consulted: 13/08/25 Catherine, M. The Search for the Largest Primes (and a Million Dollar Problem). https://www.gleammath.com/post/the-search-for-the-largest-primes-and-a-million-dollar-problem. Consulted: 14/08/25 BBC News. Largest known prime number discovered in Missouri. https://www.bbc.co.uk/news/technology- 35361090. Consulted: 15/08/25 Lesage, R. Mapping the use of computational modelling and simulation in clinics: A survey. https://pmc.ncbi.nlm.nih.gov/articles/PMC10150234/. Consulted: 16/08/25 Templeton, G. Why should we care about prime numbers? https://mashable.com/article/why-should-we-care- about-prime-numbers. Consulted: 18/09/2025
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