[QUOTE=Christenson;280327]Here's a wacky thought: The next mersenne prime to be found will be in the DCs...it had an erroneous non-zero residue turned in by someone.....it's not too wildly unlikely...especially with three different residues now on the last exponent to be DC'd below 24M....time to think about a GPU and seeing what it can do with CudaLucas...[/QUOTE]

I hope not... it'll be a while before we get to it.

[QUOTE=Christenson;280327]Here's a wacky thought: The next mersenne prime to be found will be in the DCs...it had an erroneous non-zero residue turned in by someone.....it's not too wildly unlikely...especially with three different residues now on the last exponent to be DC'd below 24M....time to think about a GPU and seeing what it can do with CudaLucas...[/QUOTE]

I suppose this would depend on the percentage of reliable first-time LL tests currently turned into the serve. There are very few (less than 200) exponents untested before M47* currently. Does anyone have any information on those that have received a first-time LL test and how many of those are suspect?

[QUOTE=Dubslow;280330]I hope not... it'll be a while before we get to it.[/QUOTE]

How does this make any difference? It is going to take a LONG time to DC all of those exponents anyway. The wait is to discover that there are missing primes or aren't any missing primes is the same. We don't have a way of knowing.

AFAIK, any tests turned in with an error code are immediately reassigned to DC workers, but of course not all bad tests report error codes. (Also, the last sentence does not make sense: Less then 200 expos untested, then ask which of those have had a test completed?)

[QUOTE=Primeinator;280335]How does this make any difference? It is going to take a LONG time to DC all of those exponents anyway. The wait is to discover that there are missing primes or aren't any missing primes is the same. We don't have a way of knowing.[/QUOTE]

Well that's what I meant, it'll be a LONG time before we figure out if we missed one. I'm confident enough in the heuristics that I don't think there are any others below M47; however, if there's another one less than 50M (which I doubt, but it's more likely than another one below 43M) it's more likely than not that we've missed it on the first go, and it could easily be a decade before we check those twice.

[QUOTE=Dubslow;280336]AFAIK, any tests turned in with an error code are immediately reassigned to DC workers, but of course not all bad tests report error codes. (Also, the last sentence does not make sense: Less then 200 expos untested, then ask which of those have had a test completed?)[/QUOTE]

I guess what I was trying to say with this is that there could (very unlikely) be an undiscovered prime below M47 that has not been LL tested once yet. Most exponents below this value have been tested at least once...it is even less likely that one of these is prime and just had a bad LL. What defines "suspect LL?" Any with an error code? I have seen these on PrimeNet.

[QUOTE=Dubslow;280338]Well that's what I meant, it'll be a LONG time before we figure out if we missed one. I'm confident enough in the heuristics that I don't think there are any others below M47; however, if there's another one less than 50M (which I doubt, but it's more likely than another one below 43M) it's more likely than not that we've missed it on the first go, and it could easily be a decade before we check those twice.[/QUOTE]

It will be a very long time indeed. Why do you feel like there aren't likely any exponents below 50M that will yield a new Mersenne? How many in this range have yet to receive a first time LL test?

[QUOTE=Primeinator;280347]What defines "suspect LL?" Any with an error code? I have seen these on PrimeNet.[/quote]
Yes, you are correct. Any error code marks it as suspect, along with immediate retesting as I said earlier.

[QUOTE=Primeinator;280347]
It will be a very long time indeed. Why do you feel like there aren't likely any exponents below 50M that will yield a new Mersenne? How many in this range have yet to receive a first time LL test?[/QUOTE]
Over the course of this project, there have been a surprising number of primes already, and given the random but average nature of their location (technical term: poisson distribution) I suspect that the next one is very far off. As for data:

[url]http://mersenne.info/exponent_status_tabular_data/2/40000000/[/url]
[url]http://mersenne.info/exponent_status_line_graph/2/40000000/[/url]

[QUOTE=Dubslow;280348]
[url]http://mersenne.info/exponent_status_tabular_data/2/40000000/[/url]
[url]http://mersenne.info/exponent_status_line_graph/2/40000000/[/url][/QUOTE]

Beautiful. I did not know you could generate reports like that.

There are still 5,000+ exponents awaiting a first time LL test in that range... statistically speaking, not great odds of finding a new Mersenne, but don't count your chickens too soon. Perhaps we have miscalculated how frequently Mersenne primes appear and they are a little more common. Increasing p by 7 million is a rather substantial jump for not finding any new primes.

The gaps between M38,M39,M40 are close to 7 million, at much lower numbers. That the following 7* are closer together seems to me that we must swing to the other side of the average, and I don't think 7M or even 10+ is unreasonable. I have half a mind to think there are none between 43M and 60M, though that is rather extreme. Of course, this is all just speculation as you pointed out.

Props to chalsall for the tool, especially the percentage graph, that's particularly awesome :)

[QUOTE=Dubslow;280352]The gaps between M38,M39,M40 are close to 7 million, at much lower numbers. That the following 7* are closer together seems to me that we must swing to the other side of the average, and I don't think 7M or even 10+ is unreasonable. I have half a mind to think there are none between 43M and 60M, though that is rather extreme. Of course, this is all just speculation as you pointed out.[/QUOTE]

This sounds like an example of the gambler's fallacy to me.

Maybe. Gambling is truly random, whereas primes are random but average.