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Research Paper | Mathematics | Uganda | Volume 11 Issue 11, November 2022 | Popularity: 5.7 / 10

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The P vs NP or P = NP Conjecture

Adriko Bosco

Abstract: The p vs np problem was first introduced by Stephen Cook in 1971 in his seminal paper, the complexity of theorem proving procedures and independently by Leonid Levin in 1973. It is one of the seven millennium prize problems selected by the Clay Mathematics Institute since 2000 each worth US$1,000,000 prize for the first correct solution. Having the solution of p = np at hand has a lot of positive implications that would change the face of the world although it has some negative impacts that can easily be fixed with time. The following are some of the importance of proving p = np. It is used in Computer Science, Computational theory, Economics e.g. Industrial production, Cryptography, Artificial Intelligence, Game theory, Philosophy etc. Some of the dangers of proving p = np include the field of cryptography which relies on certain hard problems that protect passwords. It will therefore, break most of the existing Cryptosystems such as block chain Crypto-currencies e.g. Public-key Crypto- currencies, e.g. Bitcoin, Symmetric Chippers used for encryption of communications data, Crypto-graphic system that underlines the block chain Crypto-Currencies and for software authentication.

Keywords: P versus np, algorithm, Boscomplex constant n = 1, Boscomplex theorem, probability, infinity

Edition: Volume 11 Issue 11, November 2022

Pages: 448 - 455

DOI: https://www.doi.org/10.21275/SR221029171636

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