q: Improved

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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 http://ww2.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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