Difference between revisions of "Smooth number"

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(New page: An integer is ''S-smooth'' if it does not contain any prime factors less than or equal to S. The relevance of this concept to the finding primes project is that if one inserts a non-S...)
 
 
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An integer is ''S-smooth'' if it does not contain any prime factors less than or equal to S.  The relevance of this concept to the [[finding primes]] project is that if one inserts a non-S-smooth number into a [[factoring|factoring oracle]], one will obtain a prime of size greater than S.  So it would suffice to find a small (and enumerable) set which is guaranteed to contain at least one non-S-smooth number for some large S.
 
An integer is ''S-smooth'' if it does not contain any prime factors less than or equal to S.  The relevance of this concept to the [[finding primes]] project is that if one inserts a non-S-smooth number into a [[factoring|factoring oracle]], one will obtain a prime of size greater than S.  So it would suffice to find a small (and enumerable) set which is guaranteed to contain at least one non-S-smooth number for some large S.
  
# [http://en.wikipedia.org/wiki/Smooth_number The Wikipedia entry on smooth numbers]
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* [[wikipedia:Smooth_number|The Wikipedia entry on smooth numbers]]

Latest revision as of 17:39, 19 August 2009

An integer is S-smooth if it does not contain any prime factors less than or equal to S. The relevance of this concept to the finding primes project is that if one inserts a non-S-smooth number into a factoring oracle, one will obtain a prime of size greater than S. So it would suffice to find a small (and enumerable) set which is guaranteed to contain at least one non-S-smooth number for some large S.