M43 discovery date - Page 3

ppo · 2005-12-23, 09:06

Quote:

Originally Posted by Prime95

Digging through the server logs paints an even more complex picture!

The prime was found on 12/15 at 8:43 AM local time.

Let's call this step #0
At any time after #0 the discoverer could have known that a prime was found,
so I think that this is the true time of discovery. All what happened after that was just a matter of notification to other people.

Numbers · 2005-12-23, 09:40

There is a precedent here.
In January 1952 a computer operated by Derek Lehmer found that 2^521 –1 is prime. This was during the night and the print-out was not read by anyone until the following morning. By this time the computer had also found that 2^607 –1 is prime. Lehmer read the print-out of the second prime before he read the first and so 2^521 – 1 was never officially the highest known prime. The date of discovery is given as 30 Jan 1952, the date on which Lehmer read the print-out, and the discoverer is credited as being Raphael Robinson who wrote the programme that found the numbers. Robinson never even saw the computer.

Therefore, I think the date of discovery should be the date on which a human knew what the number was.

Kudos to George, to GIMPS, and Seasons Greetings to all.

ppo · 2005-12-23, 10:15

Quote:

Originally Posted by Numbers

There is a precedent here.
In January 1952 a computer operated by Derek Lehmer found that 2^521 –1 is prime. This was during the night and the print-out was not read by anyone until the following morning. By this time the computer had also found that 2^607 –1 is prime. Lehmer read the print-out of the second prime before he read the first and so 2^521 – 1 was never officially the highest known prime. The date of discovery is given as 30 Jan 1952, the date on which Lehmer read the print-out, and the discoverer is credited as being Raphael Robinson who wrote the programme that found the numbers. Robinson never even saw the computer.

Therefore, I think the date of discovery should be the date on which a human knew what the number was.

Kudos to George, to GIMPS, and Seasons Greetings to all.

We don't know if the discoverer knew at #0, and, unless there is an early disclosure, we will not know until after verification is completed, so we should assume that he did, unless George positively knows that this is not what happened. In the case of Lehmer, we know that no one did read the printout before 30 Jan 1952. We could also take a different approach, and decide that the date of discovery is when the official verification is performed..., but that is not what has been done in the past.

akruppa · 2005-12-23, 10:23

I think this discussion is moot while we don't have a clear and generally accepted definition of "discovery". First off, discovery isn't something that happens to an object, it is an act between an observer and an object. There's no sense in saying "M43 was discovered". The computer (if we allow it to play the role of an observer) discovered M43 when it arrived at the zero residue. The primenet server discovered it later, the first human discovered it later still. The general public hasn't discovered the new prime yet.

I think we should write about who found out about whan when if we are to give dates of discovery. If we want to narrow down the story of M43 to a single date, any one seems as good as any other to me.

Alex

ppo · 2005-12-23, 12:31

I think there is a problem here, that should possibly be settled before a 10million prime is discovered, because of the rules about the distribution of money.
If for some reason no human being sees the discovery before something like #5 in George's post happens, who will be declared as the "discoverer" ?
As you can see it is not only a question of "when".

F960897 · 2005-12-23, 12:54

I agree alex on this. Both days (15th and 16th) seem fine to me. I think the day the user reads his email would not be a good idea, because during past discoveries the discoverer would read his email well after several people have figured it out.

For consistency a rule should be created on what day should be credited for the discovery. I would say in the case gimps, machine discovery date would be the way to go. But that is my personal preference based on this situation, no real compelling reasons why.

Mike Eaton

BotXXX · 2005-12-23, 13:16

I would say as a discovery date it should be the date/time reported to the server. The moment the client that found the prime makes a contact with the server. That way it is 'discovered' by the gimpsnetwork/server.

In case it would be the client. What would happen after the program finds the prime, but seconds later has a harddrive failure. The unknown prime is a mersenne prime but not know. And also not discovered. I would say the time of communication to the network is the 'discover' time.

Orgasmic Troll · 2005-12-23, 13:25

Quote:

Originally Posted by Me, in the other thread

Okay, since mathematical discovery relies on the ability to prove the result and convince others in the mathematical community that the result is true, I think that discovery needs to be from the point that someone who understands why the algorithm proves a candidate is prime sees verification that it is prime. If a janitor walked by and saw the printout "XYZ is prime" but doesn't understand it, all they have discovered is a printout saying "XYZ is prime" .. if he had stumbled across someone's screensaver that said "12345 is prime" (and believed it) they wouldn't have discovered that 12345 is prime and thus wouldn't be able to convince the mathematical community of the truth that XYZ is prime.

Although I guess, philosophically, GIMPS has never proven a number to be prime, just proven the candidates to be EXTREMELY likely to be prime. (Suppose cosmic rays interfered with the computer and all the double-checks in such an extraordinarily coincidental way that all of them erroneously reported a candidate as prime), however, the probability that GIMPS has reported a composite candidate as prime is so laughably low that it is convincing to the mathematical community, so I think my argument still holds.

emphasis added

alpertron · 2005-12-23, 13:41

Following your reasoning, it is possible that the Lucas-Lehmer has the same bug in both programs giving the same bogus residue zero. A different algorithm should be coded in order to circumvent this problem.

The only way to prove that the Mersenne number is prime is the LL test. But I think that if someone runs a Miller-Rabin test (with base different of 2 of course) the confidence will grow even if the algorithm is probabilistic. This is because the intermediate numbers are completely different from the numbers computed in the LL test and that the probability that a composite number of that size passes this test is extremely small.

Orgasmic Troll · 2005-12-23, 14:13

Quote:

Originally Posted by alpertron

Following your reasoning, it is possible that the Lucas-Lehmer has the same bug in both programs giving the same bogus residue zero. A different algorithm should be coded in order to circumvent this problem.

The only way to prove that the Mersenne number is prime is the LL test. But I think that if someone runs a Miller-Rabin test (with base different of 2 of course) the confidence will grow even if the algorithm is probabilistic. This is because the intermediate numbers are completely different from the numbers computed in the LL test and that the probability that a composite number of that size passes this test is extremely small.

First, I would like to emphasize that the second paragraph is rather inconsequential, just a philosophical note. I didn't say that that the LL test has a bug, I'm saying that because we are using machines to perform them and there is no way to reproduce the results without using a machine, there is the (extremely) minute chance that some random error (a neutrino hits the motherboard, or whatever) goes undetected.

The main point is that mathematical discovery depends upon acceptance by the mathematical community, thus for some result to be discovered, it has to be discovered by someone who can convince the mathematical community.

alpertron · 2005-12-23, 14:26

Quote:

Originally Posted by TravisT

First, I there is the (extremely) minute chance that some random error (a neutrino hits the motherboard, or whatever) goes undetected.

The chance that both Prime95 and the program that performs the verification have a bug in the same place is much greater than the event you mention above. We think that these programs are bug-free, but this is not proved.

That's why it is needed that the verification program uses another algorithm than the original program. This method is normally used when some people makes their computers find the first trillion digits of $\pi$ or similar computations.

View Poll Results: What should be the official discovery date of M43?
Dec. 15	28	52.83%
Dec. 16	25	47.17%
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2005-12-23, 09:40	#24
Numbers Jun 2005 Near Beetlegeuse 388₁₀ Posts	There is a precedent here. In January 1952 a computer operated by Derek Lehmer found that 2^521 –1 is prime. This was during the night and the print-out was not read by anyone until the following morning. By this time the computer had also found that 2^607 –1 is prime. Lehmer read the print-out of the second prime before he read the first and so 2^521 – 1 was never officially the highest known prime. The date of discovery is given as 30 Jan 1952, the date on which Lehmer read the print-out, and the discoverer is credited as being Raphael Robinson who wrote the programme that found the numbers. Robinson never even saw the computer. Therefore, I think the date of discovery should be the date on which a human knew what the number was. Kudos to George, to GIMPS, and Seasons Greetings to all.

2005-12-23, 10:23	#26
akruppa "Nancy" Aug 2002 Alexandria 2,467 Posts	I think this discussion is moot while we don't have a clear and generally accepted definition of "discovery". First off, discovery isn't something that happens to an object, it is an act between an observer and an object. There's no sense in saying "M43 was discovered". The computer (if we allow it to play the role of an observer) discovered M43 when it arrived at the zero residue. The primenet server discovered it later, the first human discovered it later still. The general public hasn't discovered the new prime yet. I think we should write about who found out about whan when if we are to give dates of discovery. If we want to narrow down the story of M43 to a single date, any one seems as good as any other to me. Alex

2005-12-23, 12:31	#27
ppo Aug 2004 italy 113 Posts	I think there is a problem here, that should possibly be settled before a 10million prime is discovered, because of the rules about the distribution of money. If for some reason no human being sees the discovery before something like #5 in George's post happens, who will be declared as the "discoverer" ? As you can see it is not only a question of "when".

2005-12-23, 12:54	#28
F960897 Dec 2005 4₁₀ Posts	I agree alex on this. Both days (15th and 16th) seem fine to me. I think the day the user reads his email would not be a good idea, because during past discoveries the discoverer would read his email well after several people have figured it out. For consistency a rule should be created on what day should be credited for the discovery. I would say in the case gimps, machine discovery date would be the way to go. But that is my personal preference based on this situation, no real compelling reasons why. Mike Eaton

2005-12-23, 13:16	#29
BotXXX Aug 2003 Europe C2₁₆ Posts	I would say as a discovery date it should be the date/time reported to the server. The moment the client that found the prime makes a contact with the server. That way it is 'discovered' by the gimpsnetwork/server. In case it would be the client. What would happen after the program finds the prime, but seconds later has a harddrive failure. The unknown prime is a mersenne prime but not know. And also not discovered. I would say the time of communication to the network is the 'discover' time.

2005-12-23, 13:41	#31
alpertron Aug 2002 Buenos Aires, Argentina 2×683 Posts	Following your reasoning, it is possible that the Lucas-Lehmer has the same bug in both programs giving the same bogus residue zero. A different algorithm should be coded in order to circumvent this problem. The only way to prove that the Mersenne number is prime is the LL test. But I think that if someone runs a Miller-Rabin test (with base different of 2 of course) the confidence will grow even if the algorithm is probabilistic. This is because the intermediate numbers are completely different from the numbers computed in the LL test and that the probability that a composite number of that size passes this test is extremely small.