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Encyclopedia > Factorization

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Factorization using the Elliptic Curve Method (618 words)
The final value must have 10000 or fewer digits, intermediate results must have 20000 or fewer digits and in the case of divisions, the dividend must be multiple of the divisor.
In order to do it, run the factorization in the first computer from curve 1, run it in the second computer from curve 10000, in the third computer from curve 20000, and so on.
When the number to be factorized is in the range 31-90 digits, after computing some curves in order to find small factors, the program switches to SIQS (if the checkbox located below the applet enables it), which is an algorithm that is much faster than ECM when the number has two large prime factors.
Factoring Numbers (685 words)
This accidental over-duplication of factors is another reason why the prime factorization is often best: it avoids counting any factor too many times.
So it's best to stick to the prime factorization, even if the problem doesn't require it, in order to avoid either omitting a factor or else over-duplicating one.
The nice thing about this upside-down division is that, when you're done, the prime factorization is the product of all the numbers around the outside.
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