Changes http://wiki.axiom-developer.org/329ErrorInIntegerFactor/diff
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??changed:
- Summary:
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-As first reported by anonymous, factoring 12399! produces a composite number
as a prime factor. Subsequently, experimenting with different versions of Axiom
exhibits some "small" composite integers that the factor programs in several
open source versions tested are unable to factor and yet the programs prime?
give correct answers. Two example numbers are:
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-\begin{axiom}
-factor 119643463
-prime? 119643463
-factor 129864979
-prime? 129864979
-\end{axiom}
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-<br>
-For the record, 119643463 = (10111)(11833) and 1129864979 = (11027)(11777).
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-The algorithms for identifying a composite integer and its factors are
probabilistic. The algorithms implemented in Axiom are in the packages PRIMES
and INTFACT (see intfact.spad) where the possibility of failure (that is,
identifying a number as prime when it is composite) is acknowledged. In the
case of primality test, the probabilities of error are given. The program
'prime?' is guaranteed to be correct for integers less than 341550071728321
with an error probability less than 4^(-10) or approximately 1 in a million.
The program 'factor' does not include failure probabilities, but failure
frequency is apparently much higher and failure can happen for even much
smaller numbers.
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-Please be aware that due to the randomness of the algorithms, the "live"
computation may result in outputs different from those observed by the original
authors.
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-Thanks to Bill Page for fixing the display problems, which is apparently due
to use of LaTeX tags involving 'verbatim'. Using html tags involving 'pre'
without embedded blank lines also seem to work.
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+Page merged with [329 FuzzyErrorInFactor]
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