Holy new Mersenne prime, Batman! (M47 related)

[jinydu]

Originally Posted by retina

This says EAF3CDC92C6F318D

... which is not the residue that was given to M32582657.

Am I forgetting something here? I thought that the unverified Mersenne prime would be given the true residue of the swapped exponent.

Thanks retina

[retina]

Originally Posted by jinydu

I thought that the unverified Mersenne prime would be given the true residue of the swapped exponent.

That would make it too easy to find the real exponent. Simply test the exponent with the fake residue to get the real residue and then a basic search in the archive to find the swapped residue would reveal the true exponent. One assumes "they" already thought of that.

[retina]

Here's a silly thought. Looking at the M44 data suggests to me that the server waited until the first LL (non double check) exponent came in that was <10M digits and then placed the fake residue. If that is how the code logic works, then it might point to the exponent immediately before the "fake" exponent?

[jinydu]

Originally Posted by retina

That would make it too easy to find the real exponent. Simply test the exponent with the fake residue to get the real residue and then a basic search in the archive to find the swapped residue would reveal the true exponent. One assumes "they" already thought of that.

I guessed "they" would have thought that by the time the exponent with the fake residue was finished testing, the verification would be finished. Apparently I was wrong and either:

1) The residue given to the real exponent is not based on the true residue of the exponent with the faked residue.

or

2) The residue given to the real exponent goes through further encryption. If you believe this option, then there must be a way to turn EAF3CDC92C6F318D into 663C8660956654.

Anyone know?

Originally Posted by cheesehead

Not even 2648A8AD8385FF__ ?

I just finished loading cleared.txt and I can confirm that no exponent on that page is reported with that residue.

[jinydu]

Originally Posted by retina

Here's a silly thought. Looking at the M44 data suggests to me that the server waited until the first LL (non double check) exponent came in that was <10M digits and then placed the fake residue. If that is how the code logic works, then it might point to the exponent immediately before the "fake" exponent?

Actually, 28829407, 42801739 and 42760397 are all consistent with that hypothesis.

[retina]

Originally Posted by jinydu

Actually, 28829407, 42801739 and 42760397 are all consistent with that hypothesis.

Yep, that would narrow the option to 3 possibles.

[ixfd64]

Is anyone testing M28829407 at the moment?

[retina]

Originally Posted by jinydu

Actually, 28829407, 42801739 and 42760397 are all consistent with that hypothesis.

And perhaps we can eliminate 28829407? Since the previous sleuthing here with regard to completion times would seem to suggest that the exponent is >10M digits.

[jinydu]

Originally Posted by ATH

M44: http://www.mersenneforum.org/showthread.php?t=6290
It was the first time they put the fake algorithm residue on the wrong exponent

M43: http://www.mersenneforum.org/showthread.php?t=5139
They put fake algorithm residue on the real M43. Some people guessed it.

M42: http://www.mersenneforum.org/showthread.php?t=3727
They put fake algorithm residue on the real M42. Exponent was guessed in post #11.

M41: http://www.mersenneforum.org/showthread.php?t=2475
They put fake algorithm residue on the real M41. See post #75-87. PrimeCruncher was the big sleuther.

M40: http://www.mersenneforum.org/showthread.php?t=1420
They put fake algorithm residue on the real M40. GP2 was the big sleuther. Residue wasn't posted but see post #86 in M41 thread.

M39: They put fake algorithm residue on the real M39. See post #86 in M41 thread.



Nov 27th 2003, just after M40: http://www.mersenneforum.org/showthread.php?t=1508
GP2 reveals his sleuthing techniques. Old man PrimeNet reveals the algorithm, and promises residue will be more random next time (M41).

I think I read somewhere that sometimes earlier than M39 they put actually 0x00000000000000000 in cleared.txt so everyone could see?

Bump. And I might also add that the residue of M38 was not disguised at all.

Originally Posted by retina

Here's a silly thought. Looking at the M44 data suggests to me that the server waited until the first LL (non double check) exponent came in that was <10M digits and then placed the fake residue. If that is how the code logic works, then it might point to the exponent immediately before the "fake" exponent?

Another thought: It could be that the fake residue is assigned to the next first-time exponent that is less than the real exponent. That would leave 42801739 and 42760397 as the only possibilities.

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To other sleuthers: At the risk of sounding repetitive... The residue given to the real M44 was 663C8660956654. How do you think this was generated?

If it was not generated randomly, this could open up a new line of attack...

[Mini-Geek]

Originally Posted by retina

Here's a silly thought. Looking at the M44 data suggests to me that the server waited until the first LL (non double check) exponent came in that was <10M digits and then placed the fake residue. If that is how the code logic works, then it might point to the exponent immediately before the "fake" exponent?

If this is correct, this strategy can't work for long, since pretty soon there will be no more <10M digits that haven't been tested once, and much earlier (likely before discovery of M46) they will be so sparse in completing that it won't be useful. This would mean that even if we figure out precisely what everything here is, it probably won't be useful in the future.

Another possibility that would result in the same three candidates: It chooses the smallest of the exponents first-time LLd after the prime is found. This is consistent with M44s results (note from the M44 thread that 14976869 was indeed a double check, I think it was listed as LL since the results disagreed or something like that).

[retina]

Originally Posted by Mini-Geek

If this is correct, this strategy can't work for long, since pretty soon there will be no more <10M digits that haven't been tested once, and much earlier (likely before discovery of M46) they will be so sparse in completing that it won't be useful.

Yes you are right about the sparseness, but I think it really doesn't matter since the lack of a fake residue[1] doesn't mean much. Indeed the lack of a fake residue would give less clues as to where/when the genuine exponent is.

[1] Here by "fake residue" I mean the residue that we can all recognise with the known algorithm. This does not include the as yet unknown algorithm that is used for the genuine exponent.