Predict "M51" (discussion)

[ET_]

Originally Posted by George M

It seems like 2^2252945257 - 1 may be prime. It has a probability of 63.7945% of being prime!!

Not quite The percentage is referred to the probability to get a factor given the exponent and its level of factorization.
In other words, you should bring the factorization of such exponent from 64 to 85 bitsbefore reasonably try a primality test.

[George M]

A question that boggled me was the following: If we have the expression 2^p - 1, do there exist two adjacent primes p_n and p_(n + 1) such that they will generate a mersenne prime on the condition that p > 19? Well, the I found it very unlikely.... but not as unlikely until I came across three candidates.

p_n = 3121238909
p_(n + 1) = 3121238921
p_(n + 2) = 3121238963

Remarkable.

[George M]

Originally Posted by ET_

Not quite The percentage is referred to the probability to get a factor given the exponent and its level of factorization.
In other words, you should bring the factorization of such exponent from 64 to 85 bitsbefore reasonably try a primality test.

Oh. Ok then. Thanks for that, so I know in the future :)

[George M]

Originally Posted by George M

Also, after looking at the 46th and 47th mersenne prime and the gap between both exponents, I consider my previous guess reasonable, but it doesn’t mean anything if M_n is factored, my previous guess being equal to n.

Ignore this, for I was misunderstood, and didn’t realise my previous guesses were indeed quite very large for M51.

[Uncwilly]

Originally Posted by ET_

1824261419 has a factor

That is your third guess that has a known factor. Thus you must wait 60 days to make another guess. No guess before March 1 will be acknowledged.

Please take your discussion to another thread and stop polluting this thread with your lack of learning.

[George M]

Originally Posted by Uncwilly

That is your third guess that has a known factor. Thus you must wait 60 days to make another guess. No guess before March 1 will be acknowledged.

Please take your discussion to another thread and stop polluting this thread with your lack of learning.

Ok, ok. I don’t mean to “pollute” this thread. It is obvious that my intentions aren’t to spam and display my “lack of learning” as you put it. I believe I am allowed to express my curiosity when appropriate and necessary, and I also believe I have done just that. I didn’t think any problem of it, and didn’t know you would have a problem with my discussion either.

If you don’t want to participate in a discussion like that, then ok. But, I personally don’t consider it as a means of pollution. In other words, there are nicer ways to say things in order to get a point across...

[Uncwilly]

Originally Posted by George M

If you don’t want to participate in a discussion like that, then ok. But, I personally don’t consider it as a means of pollution. In other words, there are nicer ways to say things in order to get a point across...

I suggested a venue for discussion, repeatedly. (You have your own domain for things like this. It was given to you gratis.) You did not check that your guess conformed with the rules (i.e. #4). You did not check to see if the number that you started to invest time in running LL, had a factor. You could have pm'ed me for an explanation. Prior examples showed that it takes a lot to get you to see things.

Lurk more. Post less. Read The Fine Websites (the Forum, the Wiki, PrimeNet, and others that are commonly linked to).

Posting a number (the p in 2^p-1) that is prime shows that you have checked at least a little, so that your number might be a prime. Checking that there are no known factors (and that it does not have 2 matching LL's) shows that your number hasn't been proven composite. If you are trying to guess at a prime, why waste your (and everyone else's) time on a known composite? Also, consider what the likelihood is that the number will get a clean LL result before another number does (that is also prime). Guessing 223,456,781 might be less wise than 332,199,893. I will leave it to you to try to figure out why.

By all means learn. But try to learn in threads and sub-fora that are designed for that. Don't play ball in the parlor.

With regards to nicer ways. The first time you posted a guess, I pointed out that it had a known factor and left it as an exercise (work, a project, something for effort to be put toward) for your to figure out about. George M jumped in quickly with 2 more guesses with out learning that lesson, or asking for pointers (which people gave, but it looks like looks like they weren't heeded), just demonstrates that you and he needed a wake-up call. Being a bit more rough can make the learner stop and take stock. Consider that we may get sharp to get to the point more quickly.

[Uncwilly]

Rule conforming guesses go over in this thread:
http://mersenneforum.org/showthread.php?t=22879

Random discussion and long winded posts make it hard to find the guesses. We have seen guesses get lost in discussion before.
Also, if posting a guess there, just you plan simple text. Also, make sure any dates posted are clear (various parts of the planet use different date conventions [is 1/9/2019 in January or in September?]).

[M344587487]

There can be only one ISO8601

[GP2]

Originally Posted by Uncwilly

Also, consider what the likelihood is that the number will get a clean LL result before another number does (that is also prime). Guessing 223,456,781 might be less wise than 332,199,893.

A valid point, but... the Mersenne primes in the 30M range were found after the ones in the 20M range. Just because you search somewhere first, doesn't mean you'll actually find something there.

And that happened despite what turned out to be an exceptionally target-rich environment, with 12 primes (so far) in the 10M to 100M range. The 100M to 1G range might revert to the mean, and could have as few as 4 primes.

And this time around the monetary incentive is only 50% higher, which is nice, but it won't drastically inflate the number of prize seekers compared to last time.

In the end, the only legacy of chasing after EFF money was a big sustained spike in the error rate when people overclocked their inadequate hardware, as seen in the graphs posted by patrik. (There were even bigger but much narrower error spikes in the upper half of the 10M range, I think maybe that was the infamous version 17 shift bug?)

In any case, my own guess of 282,362,693 assumed a near-worst case ratio between successive Mersenne primes not far from the historical 521/127 = 4.10, and the distant date of March 3, 2025 took into account the fact that resources will be diverted by some people searching a higher range first.

Edit: in case anyone is wondering what happened with M37,156,667, apparently it was churned several times and the eventual discoverer only ran his computer for 6 to 8 hours a day to save electricity:

[Uncwilly]

Originally Posted by GP2

In any case, my own guess of 282,362,693 assumed a near-worst case ratio between successive Mersenne primes not far from the historical 521/127 = 4.10, and the distant date of March 3, 2025 took into account the fact that resources will be diverted by some people searching a higher range first.

521 and 127 are small numbers compared to what we are working on now. Who knows, maybe our new level of success is the norm. It could be that the curve bends lower....