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around 200 BCE

The Sieve of Eratosthenes

Finding the primes by crossing out everything that isn’t

The sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit by crossing out multiples of numbers.

The Sieve of Eratosthenes

The earliest known reference to the sieve of Eratosthenes for finding prime numbers is in Introduction to Arithmetic by Nicomachus of Gerasa (60–120 CE), which describes it and attributes it to Eratosthenes of Cyrene (around 276–194 BCE), a Greek mathematician. Nicomachus was translated into Arabic by Thābit ibn Qurra (d. 901).

Artifact format

Unknown (lost)

Original artifact location

Kyrene (historical name), Sahhat, Libya (current name)


Primes timeline The Sieve of Eratosthenes Cataldi's Divisor Table Guldin's Factor Table Van Schooten's Prime Table Turing's Zeta Function Machine SWAC Computes New Mersenne Primes

Interactive Content

Computational Explanation

Other Resources

Additional Reading

  • D'Ooge, M. L. (trans.). Nicomachus of Gerasa: Introduction to Arithmetic. With Studies in Greek Arithmetic by Frank Egleston Robbins and Louis Charles Karpinski. New York: Macmillan, 1926.
  • Hoche, R. (trans.). Nicomachi Geraseni Pythagorei Introdvctionis arithmeticae libri II. Leipzig, Germany: Teubner, 1866.
  • Horsley, Rev. S. "Κόσκινον Ερατοσθένους or, The Sieve of Eratosthenes. Being an Account of his Method of Finding all the Prime Numbers." Philosophical Transactions of the Royal Society of London (1683–1775), Vol. 62, pp. 327–347, 1772.
  • Kutsch, W. (Ed.). Ṯābit B. Qurra's arabische Übersetzung der 'Arithmētikē eisagōgē' des Nikomachos von Gerasa. Beyrouth: Imprimerie Catholique, 1959.
  • Pappas, T. The Joy of Mathematics: Discovering Mathematics All Around You. San Carlos, CA: Wide World Publishing/Tetra, pp. 100–101, 1989.