Jasong::smile:
A quicker "get rich quick" scheme is to pick lottery numbers

[QUOTE=davieddy;113897]Jasong::smile:
A quicker "get rich quick" scheme is to pick lottery numbers[/QUOTE]
Admittedly, other than figuring out the bottom portion of his spreadsheet, I haven't really investigated the top. But have you examined his spreadsheet at least to the extent I have?

For all many of the flamers on here know, he could've up with 'reverse-sieve,'
a method that severely cuts down on the numbers that need to be tested, by identifying the numbers most likely to yield a prime.

Nobody that I know of has a way of finding new primes except the tried and true method of picking a specific k or n, deciding +1 or -1, and then sieving the alternate value of the first choice. Any new way to improve on this, even a not-so-dependable one, would be a fabulous achievement.

Cochet might be a crank, but I don't think anybody has examined his spreadsheet well enough to figure out how the numbers are generated, so even if he's wrong, you guys haven't impressed me one little bit. In this day and age, if you're good with statistics, you possess an extremely valued skill. If cochet thinks he's found something and is wrong, he's in a huge, generally more intelligent than usual club.

I'm going to spend the next 15min to 2hrs examining his spreadsheet. If I see the same patterns he claims exists, I'm going to become a full supporter of the 'cochet method,' as opposed to simply getting mad at what appears to be an online mob who like to laugh at people that they think are stupid.

[QUOTE=jasong;113943]what appears to be an online mob who like to laugh at people that they think are stupid.[/QUOTE]

Appearances are in the eye of the beholder. But [I]I[/I] don't see that as a fair description of the treatment cochet has received here.

It's a known fact that although the human brain is good at picking out patterns, when faced with patternlessness, it is suscecptible to falsely identifying patterns where none exist. It's also known that prestigious names in mathematics, such as Pomerance and Wagstaff have expressed opinions that there is no pattern in the Mersennes. So, given someone with no mathematical history that says "I see a pattern" - what do I do?

I ask for a forecast based on the pattern. If it fails and I'm feeling polite, I ask for another. and another. and another. and another. At some point I become convinced the pattern seer is mistaken, and I stop asking for another forecast.

Now if the forecasts had been correct, I would investigate the methodology, But life is too important to investigate methods that don't work. I could generate a dozen methods that don't work, and a plausible explanation for each.

So the only remaining issue is how much effort to put into convincing the seer that he is mistaken - his patterns don't really exist. The long list of failed forecasts hasn't dissuaded him. I have no stronger argument than "given multiple fair chances it always failed," and he hasn't found that persausive, so I see no point in pushing the issue. I'll ignore him until he goes away or makes better forecasts.

Predicting Mersenne primes
 

For my sins, I spent 6 months trial factoring and
LL testing up to M29 (discovered in 1988) on a K6
with my own assembler/high school multiplication programs.

An obvious predictor seemed to to be "perhaps Mersenne
primes are more likely to be found on islands of successive
prime exponents with no factors below 2^~50".

However I bowed to the numerous people who have looked into
it deeper than I have (or perhaps even could)

David

[QUOTE=davieddy;113979]up to M29 ... "perhaps Mersenne
primes are more likely to be found on islands of successive
prime exponents with no factors below 2^~50".[/QUOTE]

If you are serious about this, an obvious test would be to take the larger Mersenne primes and look at factors for the two prime exponents immediately preceeding and immediately following them.

[QUOTE=cochet;113687]... finally someone has understood why I proposed 37197833 ...[/QUOTE]

It has not been double checked yet but 37197833 has been LL tested once already and shown as not prime.

Check out [url]http://www.mersenne.org/status.htm[/url]
Near the bottom of the page are 2 lines that say:

A 19.2MB zip file of double-checked exponents and their residues.
A 4.8MB zip file of exponents that have not been verified.

Your number is NOT in the first (hence not double checked) but is in the second file (hence checked once as NOT prime)

[quote=wblipp;113980]If you are serious about this, an obvious test would be to take the larger Mersenne primes and look at factors for the two prime exponents immediately preceeding and immediately following them.[/quote]
Yes.
BTW M29 was supposed to be "the 29th Mersenne prime"(Colqitt & Welsh),
not 2^29-1 which isn't prime:smile:

[QUOTE=wblipp;113944]I ask for a forecast based on the pattern. If it fails and I'm feeling polite, I ask for another. and another. and another. and another. At some point I become convinced the pattern seer is mistaken, and I stop asking for another forecast.

Now if the forecasts had been correct, I would investigate the methodology, But life is too important to investigate methods that don't work. I could generate a dozen methods that don't work, and a plausible explanation for each.[/QUOTE]
Well, first, I'd like to say that I don't have 100%, or even 50% faith in cochet's method. But I've looked at his spreadsheet, and somewhere around M39, the numbers at the top start looking EXTREMELY similar. He's given twenty numbers that were found to be composite. But think about the failure rate of p-1. If he's found a way to conclusively reduce the number of ns that need to be tested, even by an amount as small as 2%(I chose that number randomly), he would be accomplishing something major.

I'm not saying his method works. But, with ONLY twenty misses, especially considering the number of misses needed to find each of GIMPS primes, he's at least come up with an interesting way to pick numbers to test.

[QUOTE=jasong;114013]Well, first, I'd like to say that I don't have 100%, or even 50% faith in cochet's method.[/QUOTE]
"Faith" being the operative word, because based on what we've seen so far, no rational person could have more than 0% *confidence* in the "method."

[QUOTE]But I've looked at his spreadsheet, and somewhere around M39, the numbers at the top start looking EXTREMELY similar. [/QUOTE]
Please clarify "start looking..." - are you sure it's not now *you* who is perhaps finding a pattern where none objectively exists?

[QUOTE]He's given twenty numbers that were found to be composite. But think about the failure rate of p-1.[/QUOTE]
My preferred analogy at this point is "think about the failure rate of random guessing" - in what way is p-1 a better analogy? p-1 at least is based on a well-understood mathematical technique, and is guaranteed to work under well-characterized circumstances [factor of sufficient p-1 smoothness exists].

[QUOTE]If he's found a way to conclusively reduce the number of ns that need to be tested, even by an amount as small as 2%(I chose that number randomly), he would be accomplishing something major.[/QUOTE]

We reduce the number of candidates by roughly half via trial factoring. By setting my laptop near an open window I get a speedup of 2-5% due to better airflow and a slightly cooler CPU. 2% would be "better than zero," but not what most people would call "major." And I note that this is still speaking purely hypothetically, because so far we're still stuck at 0% as far as Cochet's famous "method" goes.

[QUOTE]I'm not saying his method works. But, with ONLY twenty misses, especially considering the number of misses needed to find each of GIMPS primes, he's at least come up with an interesting way to pick numbers to test.[/QUOTE]
I'd be very interested to see what your definition of "interesting" is.

[QUOTE=jasong;114013]But, with ONLY twenty misses, especially considering the number of misses needed to find each of GIMPS primes, he's at least come up with an interesting way to pick numbers to test.[/QUOTE]

I don't really see how the method would help at all. Even if it picks slightly more promising candidates, it doesn't eliminate the need to check all candidates, so it would just shuffle the work order around, not reduce the work load.

I suggest that you should decide now how much testing is sufficient. I've already established my criterion - I'm not spending any time on this method until if has found at least one prime, and not even then unless it has happened in few enough guesses that random guessing would have less than 10% chance of succeeding.

You could pick a criteria like "I want to be 90% confident that the probability a candidate is prime is less than 2%." That's going to be a lot of tests, but we have people here that can help you figure out how many.

On the other hand, I've been day dreaming about my boast that I could invent useless methods with plausible explanations. That could be fun. How many such methods will you have the time to test for me?

William