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## RE: [PrimeNumbers] My brain hurts - finding smooth numbers on an AP

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• ... You re missing the fact that I d probably scribbled about 30 pages of notes that day (none of which were bin-fodder, it was most productive), and was quite
Message 1 of 4 , Nov 3, 2002
--- Paul Leyland <pleyland@...> wrote:
> Am I missing something?

You're missing the fact that I'd probably scribbled about 30 pages of notes
that day (none of which were bin-fodder, it was most productive), and was
quite literally mentally exhausted.

> Why don't you sieve with squares of elements from P to identify those
> not square free (by setting the location to a large negative value),

part of my approach (2)

> and then sieve the
> remaining numbers, accumulating a list of elements of P on each sieve location while adding
> log(P) to the sieve location?

my approach (1)

> After the second sieve, those locations which are approximately log(X+iY) are smooth and the
> list gives you the factorization. If you're prepared to use trial division on the smooth
> locations, you don't need to store the list while sieving.

The number that I'm expecting to pass now (I looked at a 100K range, and
found nothing) are so low that I think re-TD-ing will be inexpensive, which
was my approach (3), that it appears will play only a very minor role.

I think that (1) and (2) pretty much commute.
If anything, blanking the squaresome (neologism?) numbers after the log-accumulating
sieve works even better.

I wasn't so far out after all, I'm amazed!

It's just a shame that the yield is so low that it's probably not worth
doing. I'll put it on a back-burner, I've got another 20 pages of notes for
another new technique that may aid the task I'm currently looking at.

I'm trying to break a (minority interest) record using nothing but a single
PPro/200 - this will be a victory for wetware if it ever works!

Cheers for confirming my ideas,
Phil

=====
First rule of Factor Club - you do not talk about Factor Club.
Second rule of Factor Club - you DO NOT talk about Factor Club.
Third rule of Factor Club - when the cofactor is prime, or you've trial-
divided up to the square root of the number, the factoring is over.

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