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- \chapter{Williams' $p+1$ factorization method \label{chap:william+1}}
- Analogously to Pollard's $p-1$ factorization described in chapter
- ~\ref{chap:pollard-1}, this method will allow the determination of the divisor
- $p$ of a number $N$, if $p$ is such that $p+1$ has only small prime divisors.
- This method was presented in ~\cite{Williams:p+1} together with the results of
- the application of this method to a large number of composite numbers.
- \begin{remark}
- In the end of ~\cite{Williams:p+1}, there is a small performance comparison
- with Pollard's $p-1$:
- ``The real problem with the $p+1$ test is the fact that it is quite slow. For
- our program, we found that it was about nine times slower.''
- Nevertheless, there is no further information about the way the two
- factorization have been benchmarked.
- \end{remark}
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