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HandWiki. Generating Primes. Encyclopedia. Available online: https://encyclopedia.pub/entry/33353 (accessed on 22 September 2026).
HandWiki. Generating Primes. Encyclopedia. Available at: https://encyclopedia.pub/entry/33353. Accessed September 22, 2026.
HandWiki. "Generating Primes" Encyclopedia, https://encyclopedia.pub/entry/33353 (accessed September 22, 2026).
HandWiki. (2022, November 07). Generating Primes. In Encyclopedia. https://encyclopedia.pub/entry/33353
HandWiki. "Generating Primes." Encyclopedia. Web. 07 November, 2022.
Generating Primes
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The content is sourced from: https://handwiki.org/wiki/Generating_primes

In computational number theory, a variety of algorithms make it possible to generate prime numbers efficiently. These are used in various applications, for example hashing, public-key cryptography, and search of prime factors in large numbers. For relatively small numbers, it is possible to just apply trial division to each successive odd number. Prime sieves are almost always faster.

prime numbers hashing cryptography

References

  1. Atkin, A.; Bernstein,, D. J. (2004). "Prime sieves using binary quadratic forms". Mathematics of Computation 73: 1023–1030. doi:10.1090/S0025-5718-03-01501-1. http://cr.yp.to/papers/primesieves-19990826.pdf. 
  2. Pritchard, Paul (1994). "Improved Incremental Prime Number Sieves". Algorithmic Number Theory Symposium. pp. 280–288. 
  3. Sorenson, J. P. (1998). "Trading Time for Space in Prime Number Sieves". Lecture Notes in Computer Science 1423: 179–195. doi:10.1007/BFb0054861. https://link.springer.com/chapter/10.1007%2FBFb0054861. 
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