Computer Applications

  • John HaighEmail author


We note several important facts about prime numbers, and outline useful ideas in modular arithmetic. The ability to generate long repeatable sequences of real numbers that mimic the properties of genuinely random numbers has wide applications in game-playing, clinical trials, and any activity that requires items to be selected at random. The advantages and deficiencies of methods that have been proposed are examined. We explain why you might wish that some messages you send should be encrypted, and look at ways in which you can do so securely; the usefulness of classical results in the field of Number Theory is noted. How a computer search engine selects the order in which relevant web pages are displayed is described and illustrated.

References and Further Reading

  1. Churchhouse R F (2002) Codes and Ciphers. Cambridge University PressGoogle Scholar
  2. Diffie W and Hellman M E (1976) New Directions in Cryptography. IEEE Transactions on Information Theory 22(6) 644–54 Google Scholar
  3. Hill R (1986) A First Course in Coding Theory. Oxford University PressGoogle Scholar
  4. Knuth D E (1981) The Art of Computer Programming, Vol 2 (2nd Edition) Addison-WesleyGoogle Scholar
  5. Morgan B J T (1984) Elements of Simulation. Chapman and HallGoogle Scholar
  6. Rivest R L, Shamir A and Adelman L (1978) A method for obtaining digital signatures and public key cryptosystems. Communications of the Association for Computing Machinery Vol 21(2) 120–126Google Scholar
  7. Singh S (1999) The Code Book. Fourth EstateGoogle Scholar
  8. von Neumann J (1951) Various techniques used in connection with random digits. Monte Carlo Method, National Bureau of Standards Applied Mathematics Series 12 36–38Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SussexBrightonUK

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