## Comparing efficiency of factoring methods

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• I m wondering how my current factoring program compares to other methods used in terms of the amount of work needed to find the factors. Factored here are
Message 1 of 2 , Aug 4, 2006
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I'm wondering how my current factoring program compares to other methods
used

in terms of the amount of work needed to find the factors.

Factored here are 10^16 + 37 and 10^16+39.

The difficulty number is the number of trial difference of squares used in
the algorithm.

z = 10000000000000037 x = 168040027 y = 59509631 difficulty = 1382382
z = 10000000000000039 x = 1830629 y = 5462603291 difficulty = 655091

Kermit < kermit@... >
• ... If you really wondered how it compares to other methods, why have you not compared it to other methods? Grab Miracl, and see how quickly P-1, P+1, Rho, and
Message 2 of 2 , Aug 4, 2006
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--- Kermit Rose <kermit@...> wrote:
> I'm wondering how my current factoring program compares to other methods
> used in terms of the amount of work needed to find the factors.
>
> Factored here are 10^16 + 37 and 10^16+39.
>
> The difficulty number is the number of trial difference of squares used in
> the algorithm.
>
> z = 10000000000000037 x = 168040027 y = 59509631 difficulty = 1382382
> z = 10000000000000039 x = 1830629 y = 5462603291 difficulty = 655091

If you really wondered how it compares to other methods, why have you not
compared it to other methods?

Grab Miracl, and see how quickly P-1, P+1, Rho, and ECM can split those
numbers.

168040027 will be found by P-1, and often P+1, trivially.
59509631 will be found by P+1 trivially.
1830629 will be found by P+1 trivially.

Most things that P+/-1 can find trivially Rho and ECM can too.

Phil

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