Another interesting pattern of Mersenne exponents: they are prime!!!!1111

ProximaCentauri · 2014-12-04, 10:24

Mersenne prime exponents (except 2 and 3) follow this "pattern", or however you may call it.

There are 2 strands, the 5-strand and the 7-strand. (6n-1 and 6n+1)

Furthermore there are 8 "starting numbers", 4 for each strand.

Starting numbers for 5-strand:

5=1*6-1
17=3*6-1
107=18*6-1
756839=126140*6-1

Starting numbers for 7-strand:

7=1*6+1
13=2*6+1
19=3*6+1
2281=380*6+1

The Mersenne exponents can be described as:

p₅ⁱ=p₅⁰ + 24*n_i

p₇ⁱ=p₇⁰ + 24*n_i

My questions:

1) Are there more than these 8 "starting numbers"?
2) If question 1 can be answered with YES, how many exist?
3) Where are more, in the 5-strand or in the 7-strand?

IMHO they are exactly 50% in the 5-strand (1 mod 4) and 50% in the 7-strand (3 mod 4).

Have a look to the attached graphic and let´s discuss it!

R.D. Silverman · 2014-12-04, 10:45

Quote:

Originally Posted by ProximaCentauri

Mersenne prime exponents (except 2 and 3) follow this "pattern", or however you may call it.

There are 2 strands, the 5-strand and the 7-strand. (6n-1 and 6n+1)

Furthermore there are 8 "starting numbers", 4 for each strand.

Starting numbers for 5-strand:

5=1*6-1
17=3*6-1
107=18*6-1
756839=126140*6-1

Starting numbers for 7-strand:

7=1*6+1
13=2*6+1
19=3*6+1
2281=380*6+1

The Mersenne exponents can be described as:

p₅ⁱ=p₅⁰ + 24*n_i

p₇ⁱ=p₇⁰ + 24*n_i

My questions:

1) Are there more than these 8 "starting numbers"?
2) If question 1 can be answered with YES, how many exist?
3) Where are more, in the 5-strand or in the 7-strand?

IMHO they are exactly 50% in the 5-strand (1 mod 4) and 50% in the 7-strand (3 mod 4).

Have a look to the attached graphic and let´s discuss it!

OK. Let's discuss it.

The "pattern" you think you see is a delusion.

Try reading some books on number theory. Read Sam Wagstaff's paper on the distribution
of Mersenne primes. It would answer your "50% is 5-strand" nonsense.

Oh. And stop inventing your own terminology (e.g. "strands") It is one hallmark of
a crank. Use standard terminology.

Finally, with respect to your "IMHO", mathematics is not done by opinion.
Noone cares about your opinion. You clearly do not know enough math to
be allowed to have an "opinion".

ProximaCentauri · 2014-12-04, 11:21

Quote:

Originally Posted by R.D. Silverman

OK. Let's discuss it.

The "pattern" you think you see is a delusion.

Try reading some books on number theory. Read Sam Wagstaff's paper on the distribution
of Mersenne primes. It would answer your "50% is 5-strand" nonsense.

Oh. And stop inventing your own terminology (e.g. "strands") It is one hallmark of
a crank. Use standard terminology.

Finally, with respect to your "IMHO", mathematics is not done by opinion.
Noone cares about your opinion. You clearly do not know enough math to
be allowed to have an "opinion".

Dear R.D. Silverman

If you would have read my posting carefully you would have realized that I was not talking about Mersenne-Primes and their distribution but about the exponents yielding these Mersenne-primes!

Instead of trying to answer one or more of my questions, you started insulting me.

Don´t worry, I already read the paper of Sam and I also know very well about the distribution of Mersenne-Primes, but that does´t answer my question about the exponents, which my posting was about!

Unless you don´t have an own opinion about it, please do me a favor and stay out of this discussion!

Thanks!

bloodIce · 2014-12-04, 11:39

What you post is an open question, since there are many prime numbers of a form 6*n-1 or 6*n+1. How many of these are Mersenne-prime exponents is ongoing project in any Mersenne prime search project (such as GIMPS). Did you notice the size of the gaps between your members of a chain?

ProximaCentauri · 2014-12-04, 12:12

Quote:

Originally Posted by bloodIce

What you post is an open question, since there are many prime numbers of a form 6*n-1 or 6*n+1. How many of these are Mersenne-prime exponents is ongoing project in any Mersenne prime search project (such as GIMPS). Did you notice the size of the gaps between your members of a chain?

All primes (except 2 and 3) are of the form either 6n-1 or 6n+1, that is nothing new.

However, what´s interesting is:

What makes these 8 numbers (if they are complete) so unique?

5-17-107-756839 (5-strand acc. to my new terminology)

7-13-19-2281 (7-strand acc. to my new terminology)

Are they the building blocks of Mersenne-Primes?
Are they already complete?

Of course, the gaps (multiples of 24 added to the starting number to yield a new Mersenne prime exponent) are going bigger and bigger, as the Mersenne Primes do! That´s normal and no surprise!

This discussion is about these starting numbers, as I call them, and maybe someone can answer me, but I doubt!

science_man_88 · 2014-12-04, 12:42

Quote:

Originally Posted by ProximaCentauri

The Mersenne exponents can be described as:

p₅ⁱ=p₅⁰ + 24*n_i

p₇ⁱ=p₇⁰ + 24*n_i

why not use TEX ? so it generalizes to ${p_x}^i = {p_x}^0 +24 \times {n_i}$ ?

just double checking if the raised number are supposed to be exponents if so it generalizes to:

${p_x}^i = 1+ 24 \times {n_i}$

Quote:

My questions:

1) Are there more than these 8 "starting numbers"?

couldn't tell you if I tried and I like patterns

Quote:

2) If question 1 can be answered with YES, how many exist?

see answer 1

Quote:

3) Where are more, in the 5-strand or in the 7-strand?

see answer 1

R.D. Silverman · 2014-12-04, 12:46

Quote:

Originally Posted by ProximaCentauri

Dear R.D. Silverman

If you would have read my posting carefully you would have realized that I was not talking about Mersenne-Primes and their distribution but about the exponents yielding these Mersenne-primes!

Instead of trying to answer one or more of my questions, you started insulting me.

Don´t worry, I already read the paper of Sam and I also know very well about the distribution of Mersenne-Primes, but that does´t answer my question about the exponents, which my posting was about!

Unless you don´t have an own opinion about it, please do me a favor and stay out of this discussion!

Thanks!

Please do the rest of us a favor and stay out of this forum until you learn some math.

I do not have "opinions" about math. Despite my trying to tell you that math is not done by
"opinion", you refuse to learn.

I believe your claim about reading Wagstaff's paper to be a lie based on the level of mathematical maturity
exhibited by your posts, I apologize for suggesting that you read it. I doubt that you would understand it.

The distribution of Mersenne primes says EVERYTHING about the distribution of the exponents. You
would realize this instantly if you knew some math. (hint: think about logarithms).

I will answer your question about distribution of the exponents. The density function is the logarithmic density
of a Poisson distribution, (assuming the standard arguments about the distribution of the Mersenne primes
themselves).

Something you have to realize is the Dunning-Kruger effect. One part of it is the inability of someone
to recognize expertise in others. You claim that I did not read your posting carefully. I suggest that you
consider the possibility that some people here know so much more about the subject than you do
that it is obvious when you are prattling.

R.D. Silverman · 2014-12-04, 12:48

Quote:

Originally Posted by ProximaCentauri

All primes (except 2 and 3) are of the form either 6n-1 or 6n+1, that is nothing new.

However, what´s interesting is:

What makes these 8 numbers (if they are complete) so unique?

5-17-107-756839 (5-strand acc. to my new terminology)

7-13-19-2281 (7-strand acc. to my new terminology)

Are they the building blocks of Mersenne-Primes?
Are they already complete?

Of course, the gaps (multiples of 24 added to the starting number to yield a new Mersenne prime exponent) are going bigger and bigger, as the Mersenne Primes do! That´s normal and no surprise!

This discussion is about these starting numbers, as I call them, and maybe someone can answer me, but I doubt!

It is hard to respond to nonsense.

ProximaCentauri · 2014-12-04, 13:06

Quote:

Originally Posted by R.D. Silverman

It is hard to respond to nonsense.

Yeah, it´s hard to respond if you don´t have any clue about it! That´s correct, R.D.

ProximaCentauri · 2014-12-04, 13:21

Quote:

Originally Posted by R.D. Silverman

Please do the rest of us a favor and stay out of this forum until you learn some math.

I do not have "opinions" about math. Despite my trying to tell you that math is not done by
"opinion", you refuse to learn.

I believe your claim about reading Wagstaff's paper to be a lie based on the level of mathematical maturity
exhibited by your posts, I apologize for suggesting that you read it. I doubt that you would understand it.

The distribution of Mersenne primes says EVERYTHING about the distribution of the exponents. You
would realize this instantly if you knew some math. (hint: think about logarithms).

I will answer your question about distribution of the exponents. The density function is the logarithmic density
of a Poisson distribution, (assuming the standard arguments about the distribution of the Mersenne primes
themselves).

Something you have to realize is the Dunning-Kruger effect. One part of it is the inability of someone
to recognize expertise in others. You claim that I did not read your posting carefully. I suggest that you
consider the possibility that some people here know so much more about the subject than you do
that it is obvious when you are prattling.

I never claimed to know more than so-called experts like you, but also not less!
All I did was asking some questions which you could not answer. But it´s okay, i know number theory is a tough and dangerous ground to move.

A Poisson-distribution statistically tells you where to search for a needle in a haystack!
With other words: You know nothing where to search!

Come back to me when you have an idea on my starting numbers!

Mini-Geek · 2014-12-04, 13:24

Quote:

Originally Posted by ProximaCentauri

Yeah, it´s hard to respond if you don´t have any clue about it! That´s correct, R.D.

Brusque as he can be, RDS knows what he's talking about far more than you do in the field of mathematics.

2014-12-04, 10:24	#1
ProximaCentauri "M49" Dec 2014 Austria 2³×3 Posts	Another interesting pattern of Mersenne exponents: they are prime!!!!1111 Mersenne prime exponents (except 2 and 3) follow this "pattern", or however you may call it. There are 2 strands, the 5-strand and the 7-strand. (6n-1 and 6n+1) Furthermore there are 8 "starting numbers", 4 for each strand. Starting numbers for 5-strand: 5=16-1 17=36-1 107=186-1 756839=1261406-1 Starting numbers for 7-strand: 7=16+1 13=26+1 19=36+1 2281=3806+1 The Mersenne exponents can be described as: p₅ⁱ=p₅⁰ + 24n_i p₇ⁱ=p₇⁰ + 24n_i My questions: 1) Are there more than these 8 "starting numbers"? 2) If question 1 can be answered with YES, how many exist? 3) Where are more, in the 5-strand or in the 7-strand? IMHO they are exactly 50% in the 5-strand (1 mod 4) and 50% in the 7-strand (3 mod 4). Have a look to the attached graphic and let´s discuss it! Attached Thumbnails Last fiddled with by ProximaCentauri on 2014-12-04 at 10:38

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2014-12-04, 11:39	#4
bloodIce Feb 2010 Sweden 173 Posts	What you post is an open question, since there are many prime numbers of a form 6n-1 or 6n+1. How many of these are Mersenne-prime exponents is ongoing project in any Mersenne prime search project (such as GIMPS). Did you notice the size of the gaps between your members of a chain?