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Old 2019-04-08, 09:27   #44
ThiloHarich
 
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Nov 2005

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- Choosing the right m depends on the implementation.

Til and me used some adjustments/improvements for odd multipliers m -> in our algorithm the good multipliers are not only even, best multipliers are odd.

the numbers from nesio model : 6,12,36,60,120,360,720,1680,... do not appear in the list of good multipliers for this tuned algorithm in the top

- the number of divisors is the product of the exponents + 1 of its prime factors

If the exponents are all 1 then this is just 2^(number of prime factors of m). Having a factor with an exponent greater then one reduces the number of divisors. -> it looks like a good measure for good multipliers. But our best multiplier 315 = 3^2 * 5 * 7 has an exponent 2.

When finding the best multipliers for numbers starting at 2^54 (and only factoring numbers with factors above n^1/3) I get a complete different list then when factoring numbers starting at 2^55.

Last fiddled with by ThiloHarich on 2019-04-08 at 09:33
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