a p83 factor by ECM, the new champion

[bloodIce]

Congratulations ryanp for the nice find. It seems to me that you made your point more than clear with the recent three (or four) factors: ECM is (still) doing a great job for killing Cunningham numbers. This obviously annoys some of the big guys in the field (others are happy as everyone should be), but what to do about it. Good work, I wish you more factors.

[ixfd64]

For those who don't read the other forums, Ryan also holds the current record for finding the largest known Wagstaff PRP.

Maybe he'll also find a new Mersenne prime soon.

[sean]

Just looking for some more ways to characterize how amazing this result is.

Back in 2000, Brent published "Recent Progress and Prospects for Integer Factorisation Algorithms" which is still a good read today. Included was an empirical formula for when we could expect a particular digit level to be achieved by ECM. In particular, Brent gave:

y = 9.3 * sqrt(d) + 1932.3 where d is the number of digits and y the year.

If we plug in 83 we see that this shouldn't have happened until 2017; while a value of 77 (the second biggest so far this year) is right on target for 2013.

Another thing to note is that the product of two 83 digit numbers is well over 155 digits, so 512-bit RSA keys are now demonstrably vulnerable to ECM (not that anyone should be using keys that small and obviously gnfs is still a better choice for such keys).

[Rich]

Originally Posted by R.D. Silverman

Sam just reported that Ryan found a p83 factor of 7,337+ by
ECM !!!!!

This is truly awesome. Unless, of course, it was really done by SNFS
and Sam just made a mistake.........

It is of course possible that the factorization was done by SNFS and then the orders of lots of elliptic curves for various sigmas were calculated and trial factored until an appropriately composite one was found, The logs could then be generated by running ECM with the specific good sigma value.

This is not a trivial task but it's vastly faster to calculate the order of a curve over a p83 than it is to actually run ecm on the composite,

I suggest that a separate list of ECM records be kept where the SNFS difficulty is so high, it's obvious that the factor could only have come from ECM.

Richard

[R.D. Silverman]

Originally Posted by Rich

It is of course possible that the factorization was done by SNFS and then the orders of lots of elliptic curves for various sigmas were calculated and trial factored until an appropriately composite one was found, The logs could then be generated by running ECM with the specific good sigma value.

This is not a trivial task but it's vastly faster to calculate the order of a curve over a p83 than it is to actually run ecm on the composite,

I suggest that a separate list of ECM records be kept where the SNFS difficulty is so high, it's obvious that the factor could only have come from ECM.

Richard

You are basically accusing Ryan of fraud. I suggest that you retract your
statements immediately. Unless of course you have evidence to back
up your infammatory remarks.

I call upon the moderators to do something about this. Richard's remarks
are TOTALLY uncalled for.

[R.D. Silverman]

Originally Posted by R.D. Silverman

You are basically accusing Ryan of fraud. I suggest that you retract your
statements immediately. Unless of course you have evidence to back
up your infammatory remarks.

I call upon the moderators to do something about this. Richard's remarks
are TOTALLY uncalled for.

Let me add that the post speaks very poorly for Richard's motivations.
The fact that he believes that someone might cheat just to set a
temporary ECM record says a lot about him.

Professionals do not care about such things. Only the hacks who seek
attention and fame by accumulating "cpu credits" (and similar) have such
attitudes.

[Rich]

I'm getting mixed messages about whether you are actually serious and I wish to seek clarification of your position before replying further....

Richard

[xilman]

Originally Posted by Rich

I'm getting mixed messages about whether you are actually serious and I wish to seek clarification of your position before replying further....

Richard

That's for Bob to say.

My take is that your statement could reasonably be interpreted as an accusation. However, it could equally reasonably be interpreted as an poorly phrased hypothetical "if one wished to cheat, then .... and a list of ECM records ... should be created to draw attention to reports which deserve closer attention."

You may wish to clarify in the light of the paragraph above.

Paul

[philmoore]

Well, you did assert that it is possible that Ryan Propper cheated in obtaining his record:

Originally Posted by Rich

It is of course possible that the factorization was done by SNFS and then the orders of lots of elliptic curves for various sigmas were calculated and trial factored until an appropriately composite one was found, The logs could then be generated by running ECM with the specific good sigma value.

This is not a trivial task but it's vastly faster to calculate the order of a curve over a p83 than it is to actually run ecm on the composite.

So are you accusing him of cheating? Or are you just raising this issue to point out that it is technically possible? To raise this issue but to side-step the question of cheating seems a bit cowardly.

Originally Posted by Rich

I suggest that a separate list of ECM records be kept where the SNFS difficulty is so high, it's obvious that the factor could only have come from ECM.

This seems a rather silly suggestion, considering that the main use of running ECM to high limits is to eliminate candidates that would otherwise be factored by SNFS or GNFS.

[Mini-Geek]

Originally Posted by Rich

This is not a trivial task but it's vastly faster to calculate the order of a curve over a p83 than it is to actually run ecm on the composite,

Out of curiosity, how do you do such a thing easily? Edit: actually, on further reflection, it's pretty obvious: from p and sigma, you can calculate the group order, then simply trial factor it to ECM-like bounds and see if it reaches the bounds. You might have to TF hundreds of c83s to find one smooth enough to be realistic, but it seems pretty easy (no significant ECM or QS required on the c83s - if it's hard to factor, it won't work anyway).

Originally Posted by Rich

I'm getting mixed messages about whether you are actually serious and I wish to seek clarification of your position before replying further....

Richard

He's practically always serious, I doubt he was joking in any sense. I don't think you need to fear actually being banned based solely on your current remarks, though.

[R.D. Silverman]

Originally Posted by xilman

That's for Bob to say.

My take is that your statement could reasonably be interpreted as an accusation. However, it could equally reasonably be interpreted as an poorly phrased hypothetical "if one wished to cheat, then .... and a list of ECM records ... should be created to draw attention to reports which deserve closer attention."

It was not phrased in a hypothetical way and it was not placed in an
independent thread. It was in direct response to a discussion about the
record ECM result.