Eratosthenes Sieve

An Algorithm for making tables of Primes. Sequentially write down the Integers from 2 to thehighest number you wish to include in the table. Cross out all numbers which are divisible by 2 (every secondnumber). Find the smallest remaining number . It is 3. So cross out all numbers which are divisible by 3 (everythird number). Find the smallest remaining number . It is 5. So cross out all numbers which are divisible by 5(every fifth number).

Continue until you have crossed out all numbers divisible by , where is the FloorFunction. The numbers remaining are Prime. This procedure is illustrated in the above diagram which sieves up to 50, andtherefore crosses out Primes up to . If the procedure is then continued up to , then the number ofcross-outs gives the number of distinct Prime factors of each number.

References

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 127-130, 1996.

Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 20-21, 1996.

• Almost Alternating Link
• Almost Everywhere
• Almost Integer
• Almost Perfect Number
• Almost Prime
• Alpha
• Alphabet
• Alpha Function
• Alphamagic Square
• Alphametic
• Alpha Value
• Alternate Algebra
• Alternating Algebra
• Alternating Group
• Alternating Knot
• Alternating Knot Diagram
• Alternating Link
• Alternating Permutation
• Alternating Series
• Alternating Series Test
• Alternative Link
• Altitude
• Alysoid
• Ambient Isotopy
• Ambiguous