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q: Improved

initial writing: 2004-12-31
last updated: 2005-02-22


q: has been improved to succeed much more often. The algorithm is based on the work of Cliff Reiter on elliptic curve and other auxiliary factoring techniques as detailed in https://webbox.lafayette.edu/~reiterc/j/vector/factor_ecj.html. The algorithm starts to lose effectiveness on hard factorizations (that is, involving just two primes) of numbers with 25 digits. For example:

   x=: 8191068869406862657520989247075401x
   q: x
8191068869406862657520989247075401
   q: x* p: 1e7
179424691 8191068869406862657520989247075401
   q: x*x
|break
|       q:x*x

The last example q: x*x ran for a very long time and was interrupted by ctrl-break.

   y=: 5726527968877x
   q: y
5726527968877
   q: y*y
|nonce error
|       q:y*y

A nonce error is signalled if a composite number can not be factored by the current implementation.



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