Unique Groupings found in the first 49 mersenne numbers

[ONeil]

Originally Posted by retina

Your "analysis" is meaningless. You don't have nearly enough data points by far to come to any conclusion. Who is to say that 1 & 5 are are the "trend"? Maybe they have used up all their allotment and other numbers will come to match them? The point is that you just don't know, you simply assumed based upon a measly 49 points without any reasoning behind such an assumption.

Plus my mention of base-10 above was not addressed by you. Why base-10? Why not the residue in base-69 or base-42? What is the rationale behind base-10? How is it special that it can predict prime exponents for Mesenne numbers?

I agree that the data set is to small. Yet I maybe able to prove something here. But I would have to investigate the known primes to do this. Here is an experiment I'll just look at the first 1000 primes and exclude the mersenne primes and see what they add to in numerology. If the data set follows the mersenne trend what would that imply vs. not. Could is be possible that if I include another set of data with the mersennes would this imply anything tangible? I could just use three data sets the one I have the mixed and the the excluded mersenne set. Would you be interested in this data It would take me a couple days to produce retina?

[retina]

Originally Posted by ONeil

I agree that the data set is to small.

Good.

Originally Posted by ONeil

Yet I maybe able to prove something here. But I would have to investigate the known primes to do this.

With proper mathematical analysis or just numerology?

Originally Posted by ONeil

Here is an experiment I'll just look at the first 1000 primes and exclude the mersenne primes and see what they add to in numerology. If the data set follows the mersenne trend what would that imply vs. not. Could is be possible that if I include another set of data with the mersennes would this imply anything tangible?

Extremely unlikely. You are following in the footsteps of thousands of other people who also got nowhere.

Originally Posted by ONeil

I could just use three data sets the one I have the mixed and the the excluded mersenne set. Would you be interested in this data It would take me a couple days to produce retina?

No. It would be meaningless.

How about before you waste more time with excel, instead you explain your rationale behind the choices of base-10, and how you expect 1 & 5 to continue to be ahead in the race?

Or even simpler, explain why 3 only shows up once? Do you expect it could ever show up again? And why is there no 6? Could that ever show up in the future?

[M344587487]

It can be fun to tool around like this, but you need to understand that you're not going to make any breakthrough discoveries. If you see it as a way to exercise your mind in a mathematical context for fun, maybe even pick some numbers to LL test because of it, that's all good. Just don't obsess too much about it, and don't get disappointed when things don't pan out.

You've made two classic mistakes, a) Treating base-10 as important, and b) Ignoring variance in statistics. Even if it were true that mersenne numbers have a tendency to follow the pattern you think they do, there's nothing to show it. I'd categorise this as falling foul of the law of small numbers, but there may be something more fitting.

[ET_]

If you have a lot of time to consume, please consider studying math insteadd of numerology. Numerology is in the eye of the beholder, he and only he can see patterns that others miss. And being a subjective find, it will never be recognized by math people.

[science_man_88]

http://mathworld.wolfram.com/DigitalRoot.html

[LaurV]

Originally Posted by ONeil

I believe the graph I posted where numerology shows for P the possibility for choosing a prime number that becomes mersenne had gone up a tad; it is still shooting in the dark with now a sliver of light. It's not much, but I think I have shown a pattern where 1 and 5 could be better choices. I remain optimistic and maybe I gave you a tool.

Originally Posted by ONeil

Are you guys suggesting the data on mersenne primes for a statement that P when adding to 5 or 1 in numerology is the best choice when choosing for P is just coincidence for now? What if I'm right? Then say in another 50 years the data proves this would I be credited for taking a bit of randomness out of finding mersenne primes?

Man, you have no idea what you are talking about. Batalov tried to explain it to you but you started babbling idiocies about helping math community (giving us tools). Letting apart the fact that when I see a long string of single-digit numbers arranged vertically (and not in a comma separated list, in a "code" tag, as it would have been normal and polite) I tend to go ballistic, but letting that apart, do you understand what Serge (Batalov) is trying to tell you?

You even didn't understand the "method" you are promoting. Read again the posts.

You didn't help and didn't give us any tool, what you just "discovered" is that prime numbers can not be multiples of 3. Not interesting, and not useful at all. Go and read some wikipedia links about modular math and prime numbers before trying to make contributions.

[ONeil]

Originally Posted by LaurV

Man, you have no idea what you are talking about. Batalov tried to explain it to you but you started babbling idiocies about helping math community (giving us tools). Letting apart the fact that when I see a long string of single-digit numbers arranged vertically (and not in a comma separated list, in a "code" tag, as it would have been normal and polite) I tend to go ballistic, but letting that apart, do you understand what Serge (Batalov) is trying to tell you?

You even didn't understand the "method" you are promoting. Read again the posts.

You didn't help and didn't give us any tool, what you just "discovered" is that prime numbers can not be multiples of 3. Not interesting, and not useful at all. Go and read some wikipedia links about modular math and prime numbers before trying to make contributions.

My apologies.

[Dr Sardonicus]

Up to the limit 74207281 there are 4350601 primes. Of the 4350599 of these primes greater than 3, the residue classes 1, 5, 7, 11, 13, 17 (mod 18) [1, 5, 7, 2, 4, 8, (mod 9), resp.] contain

[725031, 725203, 724858, 725154, 725043, 725310]

of them.

Now, suppose a set of 4350599 objects is partitioned into six subsets with the above-indicated numbers of objects. Suppose 48 objects (the number of exponents greater than 3 known to yield Mersenne primes) are selected at random from the set. What is needed is, the "likely" number of elements in each of the six subsets.

Alas, it's been too many decades since I took probability and statistics. What is this, a multinomial distribution question?

At any rate, it gives a framework within which one might answer the question of how much of an "oddity" the given results may be.

"Expected" would be (I think) [8, 8, 8, 8, 8, 8]; Actual is [11, 11, 5, 7, 8, 6]

[science_man_88]

Originally Posted by Dr Sardonicus

Up to the limit 74207281 there are 4350601 primes. Of the 4350599 of these primes greater than 3, the residue classes 1, 5, 7, 11, 13, 17 (mod 18) [1, 5, 7, 2, 4, 8, (mod 9), resp.] contain

[725031, 725203, 724858, 725154, 725043, 725310]

of them.

Now, suppose a set of 4350599 objects is partitioned into six subsets with the above-indicated numbers of objects. Suppose 48 objects (the number of exponents greater than 3 known to yield Mersenne primes) are selected at random from the set. What is needed is, the "likely" number of elements in each of the six subsets.

Alas, it's been too many decades since I took probability and statistics. What is this, a multinomial distribution question?

At any rate, it gives a framework within which one might answer the question of how much of an "oddity" the given results may be.

"Expected" would be (I think) [8, 8, 8, 8, 8, 8]; Actual is [11, 11, 5, 7, 8, 6]

And the shift among 3 mod 4 would probably lean it more to what's happenng. Edit: for OP if exponent p, is 3 mod 4 and 2p+1 is prime we have it divide 2^p-1

[gophne]

Originally Posted by ONeil

I believe the graph I posted where numerology shows for P the possibility for choosing a prime number that becomes mersenne had gone up a tad; it is still shooting in the dark with now a sliver of light. It's not much, but I think I have shown a pattern where 1 and 5 could be better choices. I remain optimistic and maybe I gave you a tool.

Hi ONeil

Interesting. Off course 3, 6 & 9 won't appear because if the addition of the digits would have 3, 6 or 9 as a sum, they would be divisible by 3.

What is very interesting, but still probably not a pattern, is how many times in the list a particular sum of the digits repeats itself!

How on earth did you manage to find the sum of the digits of the higher mersenne prime numbers?

[Batalov]

Originally Posted by gophne

How on earth did you manage to find the sum of the digits of the higher mersenne prime numbers?

He didn't.
(Even though it is elementary.)