entire database done up to 2^58

[tha]

All exponents including the lowest exponents have been factored up to 2^58. Congratulations to the one(s) working on these exponents.

YotN,

Henk.

[markr]

Congratulations!
A significant milestone, after many months of work!

[lorgix]

UPDATE:

As of right now there are only 40 exponents that have not been TFd deeper than 58bits.

Here they are:

1277
1619
2377
2423
2477
2521
2557
2671
2713
2719
2851
3049
3607
3673
3691
3847
3881
3919
4007
4049
4111
4159
4261
4363
4567
4583
4591
4703
4721
5443
5471
5503
5839
5879
5923
6007
6073
6247
6581
6733

[The bold ones have been more extensively P-1-factored than the others]

[smh]

These exponents have had enough ecm that factor will be found with trail factoring is extremely small.

[lorgix]

Originally Posted by smh

These exponents have had enough ecm that factor will be found with trail factoring is extremely small.

So is [n^-1] when n→'the extreme'.

But yes, you're right.

Times like these we'd almost want to do TF backwards from the sqrt of the number to be factored.

Related example; the case of the good ol' M1061: do TF from 160b to 62b...
I realize we're not quite there yet. Obviously ECM is the most efficient method at hand.

But if someone wants to stress test an old AMD with no memory I guess they might as well give it a shot.

[Uncwilly]

Originally Posted by lorgix

But if someone wants to stress test an old AMD with no memory I guess they might as well give it a shot.

A properly set up GPU could work this over. I know that the current code was more for the higher range.

[petrw1]

Originally Posted by lorgix

So is [n^-1] Times like these we'd almost want to do TF backwards from the sqrt of the number to be factored.

Related example; the case of the good ol' M1061: do TF from 160b to 62b...
I realize we're not quite there yet.

But if someone wants to stress test an old AMD with no memory I guess they might as well give it a shot.

Not sure about the "old AMD part".
A single core of a higher-end Quad would take the better part of a full year just to TF M1061 from 62 to 63.
Considering each bit level takes twice as long as the one before; 160 Bits would take ... ummm, never mind, even from 62 up to 70 bits would take all 4 cores of the fastest PC decades.

[lorgix]

Originally Posted by petrw1

Not sure about the "old AMD part".
A single core of a higher-end Quad would take the better part of a full year just to TF M1061 from 62 to 63.
Considering each bit level takes twice as long as the one before; 160 Bits would take ... ummm, never mind, even from 62 up to 70 bits would take all 4 cores of the fastest PC decades.

That's what I meant by not quite there yet, not yet time for "backwards-TF".

But I'm thinking it (normal TF) would make sense as a hardware test;
A factor found early on is almost certainly faulty (and easy to verify), a factor found later on is easy to verify, a huge victory, and it would also suggest ones hardware is fairly stable.

[lorgix]

Btw, the concept of backwards-TF gets me thinking...

Does anyone know if an efficient non-continuous factoring method has been described? Such a method could under certain circumstances be more efficient than "continuous TF". When you don't know what you're looking for random (modified with the expected distribution of factors obv.) order beats the crap out of 'one direction'.

Am I making any sense? If so; any thoughts?

Maybe I'm missing some fatal flaw and ECM is the best viable alternative...

[axn]

Originally Posted by lorgix

When you don't know what you're looking for random (modified with the expected distribution of factors obv.) order beats the crap out of 'one direction'.

random order (modified with the expected distribution of factors) = start from the lowest and proceed higher. because a smaller prime has higher probability of being a factor than a larger one.

[lorgix]

Originally Posted by axn

random order (modified with the expected distribution of factors) = start from the lowest and proceed higher. because a smaller prime has higher probability of being a factor than a larger one.

Ok, you seem to be thinking what I'm thinking. Except I'm thinking...

In soccer the goal keeper goes left more often than right, does that mean players should ALWAYS.. you get the point.. I hope.

I haven't formally studied the right kind of math to have the language to express these thoughts.

I ofc understand that 2, 3 & 5 have a much greater chance of being divisors of a number from the set of integers, so the curve is very steep... it is nonetheless a curve.