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