Nicaraguan method for decomposing positive integers into their two prime factors, using the general quadratic formula to disseminate the impact of school mathematics in areas as important as computer security, considering the factorial dependence of

This article proposes an innovative method for factoring large integers, based on school mathematics (solving quadratic equations using the general formula). Through an algebraic transformation, the author shows that it is possible to express a composite number "m" (the product of two primes) as a quadratic equation whose solution is the prime factors. This approach theoretically reduces the complexity of the factorization problem without using advanced cryptographic algorithms or intensive computational techniques. Examples and a simple Python script that automates the process are presented. The largest number factored in this document was 22 digits (approx. 81 bits) and corresponds to the 2,580,518,811,544,498,699,793. To know the n -th positions of the prime numbers resulting in examples 1 through 3, review table no. 3 of the FNPFCP article mentioned in Note 1 on Page 2 of this document, and for examples 4 and 5 review table no. 7 in the annexes of the aforementioned article. The relevance of this study is highlighted in the context of the RSA algorithm, which bases its security on the difficulty of factoring large numbers into their prime factors. The proposed method may represent an educational breakthrough and a potential computational optimization, although not necessarily a direct threat to modern cryptography. In any case, there are many books, documents, video tutorials, and courses on the internet that expose operating system vulnerabilities, and others that teach port scanning (using Nmap, Nessus, Wireshark, etc.), virus anatomies, and cyberattacks for educational purposes. Therefore, providing this method should not pose any danger or concern compared to other topics in the world of cybersecurity. Furthermore, there are other alternatives to RSA.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-05-08
DOI
https://doi.org/10.5281/zenodo.15396994
Primary Topic
Cryptography and Residue Arithmetic
Type
article
Field-Weighted Citation Impact
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article

Nicaraguan method for decomposing positive integers into their two prime factors, using the general quadratic formula to disseminate the impact of school mathematics in areas as important as computer security, considering the factorial dependence of

Zenodo (CERN European Organization for Nuclear Research)
Cryptography and Residue Arithmetic
article

Nicaraguan method for decomposing positive integers into their two prime factors, using the general quadratic formula to disseminate the impact of school mathematics in areas as important as computer security, considering the factorial dependence of

article en

Abstract

This article proposes an innovative method for factoring large integers, based on school mathematics (solving quadratic equations using the general formula). Through an algebraic transformation, the author shows that it is possible to express a composite number "m" (the product of two primes) as a quadratic equation whose solution is the prime factors. This approach theoretically reduces the complexity of the factorization problem without using advanced cryptographic algorithms or intensive computational techniques. Examples and a simple Python script that automates the process are presented. The largest number factored in this document was 22 digits (approx. 81 bits) and corresponds to the 2,580,518,811,544,498,699,793. To know the n -th positions of the prime numbers resulting in examples 1 through 3, review table no. 3 of the FNPFCP article mentioned in Note 1 on Page 2 of this document, and for examples 4 and 5 review table no. 7 in the annexes of the aforementioned article. The relevance of this study is highlighted in the context of the RSA algorithm, which bases its security on the difficulty of factoring large numbers into their prime factors. The proposed method may represent an educational breakthrough and a potential computational optimization, although not necessarily a direct threat to modern cryptography. In any case, there are many books, documents, video tutorials, and courses on the internet that expose operating system vulnerabilities, and others that teach port scanning (using Nmap, Nessus, Wireshark, etc.), virus anatomies, and cyberattacks for educational purposes. Therefore, providing this method should not pose any danger or concern compared to other topics in the world of cybersecurity. Furthermore, there are other alternatives to RSA.

Zenodo (CERN European Organization for Nuclear Research)
Ministerio de Educación Pública (CR)
Quality Education
Openalex Percentile: Top 43%
Cryptography and Residue Arithmetic
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Nicaraguan method for decomposing positive integers into their two prime factors, using the general quadratic formula to disseminate the impact of school mathematics in areas as important as computer security, considering the factorial dependence of · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS