when is 24m+7 prime ?
 

Is there a property of x that tells when 24m+7 could be prime ? That is what I want to know today. I know [url]http://oeis.org/A139483[/url] is when it is prime but is there a way to know when it isn't prime ? If so what values wouldn't work in [url]http://oeis.org/A002450[/url] because 24m+7 with m taking on these values is what produces every odd indexed Mersenne number.

[QUOTE=science_man_88;246996]Is there a property of x that tells when 24m+7 could be prime ? That is what I want to know today. I know [URL]http://oeis.org/A139483[/URL] is when it is prime but is there a way to know when it isn't prime ? If so what values wouldn't work in [URL]http://oeis.org/A002450[/URL] because 24m+7 with m taking on these values is what produces every odd indexed Mersenne number.[/QUOTE]If you told us what "x" is, we may be able to answer you. Until then, we don't have a hope.

[QUOTE=xilman;247002]If you told us what "x" is, we may be able to answer you. Until then, we don't have a hope.[/QUOTE]

sorry typo it should be m

[QUOTE=science_man_88;247027]sorry typo it should be m[/QUOTE]

24m+7 can be prime if m != 0 mod 7

[QUOTE=R.D. Silverman;247041]24m+7 can be prime if m != 0 mod 7[/QUOTE]

Thank you, that knocks every third one from the list by the looks of it. Want me to continue further ? I see what you mean though now that knocks out all 6x+9 indexes of Mersennes the first set eliminated after the even numbers. okay so i may be able to work that out for non prime indexes so it's the indexes that can create prime exponents that gives the difficulties. you've given me a lesson i should have known but it's a nice refresher.

[QUOTE=science_man_88;247044]Thank you, that knocks every third one from the list by the looks of it. Want me to continue further ? I see what you mean though now that knocks out all 6x+9 indexes of Mersennes the first set eliminated after the even numbers. okay so i may be able to work that out for non prime indexes so it's the indexes that can create prime exponents that gives the difficulties. you've given me a lesson i should have known but it's a nice refresher.[/QUOTE]

What you are doing is pointless. For two reasons:

(1) You do not know what you are doing.
(2) It amounts to nothing more than eliminating candidates by trial
division by small potential divisors.

[QUOTE=R.D. Silverman;247049]What you are doing is pointless. For two reasons:

(1) You do not know what you are doing.
(2) It amounts to nothing more than eliminating candidates by trial
division by small potential divisors.[/QUOTE]

I know what I'm doing I thought someone was about to point out it was "pointless" 24m+7 works out to a odd indexed mersenne number if you plug in m = [url]http://oeis.org/A002450[/url]. but if you think it's pointless i guess i have no point in trying to talk to you reasonably.

[QUOTE=science_man_88;247051]I know what I'm doing
[/QUOTE]

No, you don't. You are so lacking in basic mathematical knowledge
that everything you do is essentially just noise.


[QUOTE]
I thought someone was about to point out it was "pointless" 24m+7 works out to a odd indexed mersenne number if you plug in m = [url]http://oeis.org/A002450[/url]. but if you think it's pointless i guess i have no point in trying to talk to you reasonably.[/QUOTE]

You haven't tried reason yet. All I see is nonsense.

And you also need to learn to [b]accept[/b] what experts tell you.
I am not the only one with whom you ignorantly argue.

Stop your arrogance.

[QUOTE=R.D. Silverman;247055]No, you don't. You are so lacking in basic mathematical knowledge
that everything you do is essentially just noise.




You haven't tried reason yet. All I see is nonsense.

And you also need to learn to [b]accept[/b] what experts tell you.
I am not the only one with whom you ignorantly argue.

Stop your arrogance.[/QUOTE]

from what I've seen of your personality I can say that from my experience around anyone you find less experienced you act like a bully looking for a fight while having the principal as your best friend not willing to expel you from the school.

[QUOTE=science_man_88;247057]from what I've seen of your personality I can say that from my experience around anyone you find less experienced you act like a bully looking for a fight while having the principal as your best friend not willing to expel you from the school.[/QUOTE]

On the contrary. There was an Israeli student with the math subforum
whom I very patiently led through many exercizes in high school level
mathematics as well as elementary number theory.

The difference is in [i]attitude[/i], and yours sucks. Big time.

I do admit total disdain for those (such as yourself) who are unwilling
to do any reading and learning. You are willfully ignorant.

The issue is [b]NOT[/b] "less experience" [as you claim], but a
[b]very[/b] stubborn ignorance combined with arrogance.

[QUOTE=R.D. Silverman;247058]who are unwilling
to do [B][U][I][COLOR="Red"][SIZE="7"]any[/SIZE][/COLOR][/I][/U][/B] reading and learning..[/QUOTE]

I have done a bit of reading I've even followed links to sites about a topic to learn but that didn't help me learn much.

[QUOTE=science_man_88;247060]I have done a bit of reading I've even followed links to sites about a topic to learn but that didn't help me learn much.[/QUOTE]

So tell us.

If you can not understand what you read, why do you think you have
any hope of having an intelligent discussion about mathematics???

It is sheer arrogance.

We will help you. But you need to

(1) Relate what you have read
(2) Ask specific questions about things you do not understand
(3) Do some exercizes.
(4) Present your solutions.

Stop prattling about things that you do not understand and go LEARN.

[QUOTE=R.D. Silverman;247063]So tell us.

If you can not understand what you read, why do you think you have
any hope of having an intelligent discussion about mathematics???

[COLOR="Red"]Probably stems from the fact that I seem to be one of the smartest people I know outside of on the internet.[/COLOR]

It is sheer arrogance.

We will help you. But you need to

(1) Relate what you have read

[COLOR="Red"]I've [COLOR="Orange"]tried[/COLOR] to in some of the question I've asked.[/COLOR]

Answered in short form.

(2) Ask specific questions about things you do not understand

[COLOR="Red"][COLOR="DarkOrange"]Pointless[/COLOR] as I don't have enough knowledge of the math language to phrase things obviously.[/COLOR]

(3) Do some exercizes.

Dare I point out a spelling error ? [COLOR="Red"]What [COLOR="DarkOrange"]type[/COLOR] of exercises[/COLOR]?

(4) Present your solutions.

[COLOR="Red"][COLOR="DarkOrange"]Nobody[/COLOR] can take me serious so this is also a waste of time ( though it gives me something other than cityville to do all day.[/COLOR]

Stop prattling about things that you do not understand and go LEARN.[/QUOTE]

answered in short form

[QUOTE=R.D. Silverman;247055]

And you also need to learn to [B]accept[/B] what experts tell you.
I am not the only one with whom you ignorantly argue.

Stop your arrogance.[/QUOTE]

Dear Dr. Silverman: Please, without referencing your credentials,
as I don't right now mention mine, try to prove you ARE both an
expert in Number Theory (or math) and a human being?

I'm no longer sure about the former because your attitude is
convincing of the opposite of the latter.

Yours truly -

----------------- davar55 (Yale B.S. Math 1976 A.D.)

[QUOTE=davar55;247415]Dear Dr. Silverman: Please, without referencing your credentials[/QUOTE]

Is he allowed to cite his published work?

[QUOTE=CRGreathouse;247419]Is he allowed to cite his published work?[/QUOTE]Likewise, I can attest he's a human being.

Paul

[B]55[/B] years of birth
why not davar5[B]6[/B]


(lol)




[COLOR="LemonChiffon"]ps . Who can swear "x_il_man"[/COLOR]

[QUOTE=xilman;247427]Likewise, I can attest he's a human being.[/QUOTE]

I would be far more impressed if he were a computer. There are ~7 billion human beings alive today but ~0 AIs sophisticated enough to post coherently on forums in the manner R.D. Silverman has.

aisais
 

[QUOTE=CRGreathouse;247433]I would be far more impressed if he were a computer. There are ~7 billion human beings alive today but ~0 AIs sophisticated enough to post coherently on forums in the manner R.D. Silverman has.[/QUOTE]

CRG [B]1[/B] ?

Not meaning to threadjack - mods, zap this if it offends - but how many of you have read a proof of Dirichlet's Theorem?

It was something I managed to skip in number theory long ago, but I finally did the deed last year. It was a modern proof based on Shapiro's Tauberian Theorem in Apostol's book.

That's among the top 5 nastiest proofs I've waded through. Few components were difficult to follow, but the whole thing left me feeling proud to have understood it, yet still unenlightened.

I wonder how much worse the earlier proofs are.

[QUOTE=FactorEyes;247453]Not meaning to threadjack - mods, zap this if it offends - but how many of you have read a proof of Dirichlet's Theorem?

It was something I managed to skip in number theory long ago, but I finally did the deed last year. It was a modern proof based on Shapiro's Tauberian Theorem in Apostol's book.

That's among the top 5 nastiest proofs I've waded through. Few components were difficult to follow, but the whole thing left me feeling proud to have understood it, yet still unenlightened.

I wonder how much worse the earlier proofs are.[/QUOTE]

Serre's "A Course in Arithmetic" gives a good exposition.

[QUOTE=R.D. Silverman;247058]On the contrary. There was an Israeli student with the math subforum
whom I [B]very patiently[/B] led through many exercizes in high school level
mathematics as well as elementary number theory.
[/QUOTE] (emphasis added)

BWAA-HA-HA-HA. You have got to be kidding me!
:grin::grin::grin::grin:

[QUOTE=jyb;247467](emphasis added)

BWAA-HA-HA-HA. You have got to be kidding me!
:grin::grin::grin::grin:[/QUOTE]Not in my opinion. Bob did indeed show exemplary patience during that episode.


Paul

[QUOTE=xilman;247472]Not in my opinion. Bob did indeed show exemplary patience during that episode.


Paul[/QUOTE]

I will concede that he showed far more patience during that episode than he usually does. But you don't have to search very far in that thread to see some fairly egregious examples of impatience. So calling it "exemplary" strikes me as way off. This forum is filled with explanations and responses (including some from you) that make for far better examples of how to be patient and helpful with those seeking information or improvement. For that matter, Bob himself has occasionally shown more patience than he did in that particular case. I just find it amusing that he's holding that one up as a positive example.

[QUOTE=jyb;247493]I will concede that he showed far more patience during that episode than he usually does. But you don't have to search very far in that thread to see some fairly egregious examples of impatience. So calling it "exemplary" strikes me as way off. This forum is filled with explanations and responses (including some from you) that make for far better examples of how to be patient and helpful with those seeking information or improvement. For that matter, Bob himself has occasionally shown more patience than he did in that particular case. I just find it amusing that he's holding that one up as a positive example.[/QUOTE]And yet I often lost my patience during that thread. The difference between Bob and msyelf may be that I didn't post my impatience for everyone to see. At least, not often. I hope.

Paul

Sinve RDS apparently has davar55 on his ignore list,
while davar55 definitely is not igmoring RDS (Dr. Silverman),
can I just say he's welcome to prove his worth any and
every time he chooses. And I know he's human, I meant
only that his attitude toward others is too arrogantly
intolerant. I've found his contributions important
(Sylow Theorems from group theory of basic algebra, idoneal
numbers of Euler, etc etc etc). but his insulting demeanor
irks some of you and makes him difficult to communicate with.

[QUOTE=davar55;247415]Dear Dr. Silverman: Please, without referencing your credentials,
as I don't right now mention mine, try to prove you ARE both an
expert in Number Theory (or math) and a human being?[/QUOTE]

[url]http://en.scientificcommons.org/robert_d_silverman[/url]

[url]http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/s/Silverman:Robert_D=.html[/url]

[url]http://portal.acm.org/author_page.cfm?id=81100001661&coll=DL&dl=ACM&trk=0&cfid=6755300&cftoken=68836473[/url]

[url]http://scholar.google.com/scholar?hl=en&q=r+d+silverman&btnG=Search&as_sdt=1%2C44&as_ylo=&as_vis=0[/url]

[QUOTE=axn;247590][url]http://scholar.google.com/scholar?hl=en&q=r+d+silverman&btnG=Search&as_sdt=1%2C44&as_ylo=&as_vis=0[/url][/QUOTE]

Careful, 'cuz there's a Ross D. Silverman who writes those medical articles....

I would think that if you can be "1", then that's not to be
truly "1"

Ago:sti:no:+S.

So RDS had something to do
with MPQS = Multiple Polynomial Quadratic Sieve
and
QS = Quadratic Sieve ?

That's cool.

I knew he knew some important things.
So what's the problem?

u

To cmd: by u do u mean me or the variable u?

27o°1°T
 

[QUOTE=davar55;247959]To cmd: by u do u mean me or the variable u?[/QUOTE]

sometimes the "u"to be or not to be "u" ... never
simultaneously

try to rotate the screen 270 °
if "n" then see video on the contrary

bdpq

Sometimes the light dawns slowly, even in finite quanta.

Let me propose a proposition:

If bdpqx = bdpq* and u ne n, what is io* ???

Puzzling, ain't it?

read from right to left or turn [URL="http://3.bp.blogspot.com/_rvR3ouziO8g/TCqrYcpNe6I/AAAAAAAAAnw/bzE6TQPZXQY/s1600/c_bdpq_1209_fh.PNG"]image[/URL]
and then read horizontally from left to right ...
so maybe get to 24m+7 then if u want to continue to oo

[QUOTE=R.D. Silverman;247055]No, you don't. You are so lacking in basic mathematical knowledge
that everything you do is essentially just noise.

You haven't tried reason yet. All I see is nonsense.

And you also need to learn to [B]accept[/B] what experts tell you.
I am not the only one with whom you ignorantly argue.

Stop your arrogance.[/QUOTE]

to RDS (Dr. Silverman): sm88 is trying to discover a formula for MPs
or MPEs empirically by making guesses as to what oeis and other series
might intuitively or logically be combined.

to sm88: RDS is far more arrogant than you or I (but not hopeless).

Some excerpts from this thread I think RDS should re-read:

[QUOTE=R.D. Silverman;247058]On the contrary. There was an Israeli student with the math subforum
whom I very patiently led through many exercizes in high school level
mathematics as well as elementary number theory.

The difference is in [I]attitude[/I], and yours sucks. Big time.

I do admit total disdain for those (such as yourself) who are unwilling
to do any reading and learning. You are willfully ignorant.

The issue is [B]NOT[/B] "less experience" [as you claim], but a
[B]very[/B] stubborn ignorance combined with arrogance.[/QUOTE]

[QUOTE=R.D. Silverman;247063]So tell us.

If you can not understand what you read, why do you think you have
any hope of having an intelligent discussion about mathematics???

It is sheer arrogance.

We will help you. But you need to

(1) Relate what you have read
(2) Ask specific questions about things you do not understand
(3) Do some exercizes.
(4) Present your solutions.

Stop prattling about things that you do not understand and go LEARN.[/QUOTE]

[QUOTE=davar55;247415]Dear Dr. Silverman: Please, without referencing your credentials,
as I don't right now mention mine, try to prove you ARE both an
expert in Number Theory (or math) and a human being?

I'm no longer sure about the former because your attitude is
convincing of the opposite of the latter.

Yours truly -

----------------- davar55 (Yale B.S. Math 1976 A.D.)[/QUOTE]

[QUOTE=CRGreathouse;247419]Is he allowed to cite his published work?[/QUOTE]

[QUOTE=xilman;247427]Likewise, I can attest he's a human being.
[/QUOTE]

[QUOTE=CRGreathouse;247433]I would be far more impressed if he were a computer. There are ~7 billion human beings alive today but ~0 AIs sophisticated enough to post coherently on forums in the manner R.D. Silverman has.[/QUOTE]

[QUOTE=jyb;247493]I will concede that he showed far more patience during that episode than he usually does. But you don't have to search very far in that thread to see some fairly egregious examples of impatience. So calling it "exemplary" strikes me as way off. This forum is filled with explanations and responses (including some from you) that make for far better examples of how to be patient and helpful with those seeking information or improvement. For that matter, Bob himself has occasionally shown more patience than he did in that particular case. I just find it amusing that he's holding that one up as a positive example.[/QUOTE]

[QUOTE=xilman;247494]And yet I often lost my patience during that thread. The difference between Bob and msyelf may be that I didn't post my impatience for everyone to see. At least, not often. I hope.
[/QUOTE]

[QUOTE=davar55;247504]Sinve RDS apparently has davar55 on his ignore list,
while davar55 definitely is not igmoring RDS (Dr. Silverman),
can I just say he's welcome to prove his worth any and
every time he chooses. And I know he's human, I meant
only that his attitude toward others is too arrogantly
intolerant. I've found his contributions important
(Sylow Theorems from group theory of basic algebra, idoneal
numbers of Euler, etc etc etc). but his insulting demeanor
irks some of you and makes him difficult to communicate with.[/QUOTE]

[QUOTE=davar55;247717]So RDS had something to do
with MPQS = Multiple Polynomial Quadratic Sieve
and
QS = Quadratic Sieve ?

That's cool.

I knew he knew some important things.
So what's the problem?[/QUOTE]

[QUOTE=davar55;248548]to RDS (Dr. Silverman): sm88 is trying to discover a formula for MPs
or MPEs empirically by making guesses as to what oeis and other series
might intuitively or logically be combined.

to sm88: RDS is far more arrogant than you or I (but not hopeless).[/QUOTE]

The time has come to help our RDS out of his anger and into the light.

[QUOTE=davar55;248548]to RDS (Dr. Silverman): sm88 is trying to discover a formula for MPs
or MPEs empirically by making guesses as to what oeis and other series
might intuitively or logically be combined.

to sm88: RDS is far more arrogant than you or I (but not hopeless).[/QUOTE]

he's not arrogant he obviously sees that number theory explains or dismisses what I state, this thread is simply to ask when 24m+7 is prime, if you look:

24m+7 = 6n+1 where n = 4x+1 if you look closer you can see, that for example(s) 24(0)+7 = 7, 24(1)+7 = 31, 24(5)+7 = 120+7 = 127, ... if you continues you see each m that makes a odd Mersenne number is 4x+1 where x is the previous m. If you look you'll see that [url]http://oeis.org/A002450[/url] is this sequence of m values. so by eliminating from this sequence using things like the mod 7 suggestion we can check this sequence. Note that knowing when 6n+1 could be prime helps because that imparts the properties for 24m+7 as well as say 96y+31 because they can be transmuted if you will through this sequence and hence we might be able to use a finite subsequence by changing up to the next one in this series of equations it's easily computable by taking the number into a sequence like this what values they'd take on under 6n+1 and hence tell how many odd exponents to go up to figure the exponent.

[QUOTE=science_man_88;248567]he's not arrogant he obviously sees that number theory explains or dismisses what I state, this thread is simply to ask when 24m+7 is prime, if you look:

24m+7 = 6n+1 where n = 4x+1 if you look closer you can see, that for example(s) 24(0)+7 = 7, 24(1)+7 = 31, 24(5)+7 = 120+7 = 127, ... if you continues you see each m that makes a odd Mersenne number is 4x+1 where x is the previous m. If you look you'll see that [URL]http://oeis.org/A002450[/URL] is this sequence of m values. so by eliminating from this sequence using things like the mod 7 suggestion we can check this sequence. Note that knowing when 6n+1 could be prime helps because that imparts the properties for 24m+7 as well as say 96y+31 because they can be transmuted if you will through this sequence and hence we might be able to use a finite subsequence by changing up to the next one in this series of equations it's easily computable by taking the number into a sequence like this what values they'd take on under 6n+1 and hence tell how many odd exponents to go up to figure the exponent.[/QUOTE]

Fair enough re: the math. And re: RDS.

But I didn't say he was arrogant, just moreso than you or I.

[QUOTE=davar55;248589]Fair enough re: the math. And re: RDS.

But I didn't say he was arrogant, just moreso than you or I.[/QUOTE]

Anyways davar55 knowing what you know, what do you think is the easiest way to go about this ?

[QUOTE=science_man_88;248706]Anyways davar55 knowing what you know, what do you think is the easiest way to go about this ?[/QUOTE]

Knowing what you know now, rewrite the OP as your next post,
and redirect this thread back to math.

[QUOTE=davar55;248811]Knowing what you know now, rewrite the OP as your next post,
and redirect this thread back to math.[/QUOTE]

okay I guess since you want me to. I first asked about for what m works such that [TEX] A = {A000040} \cap {A135659(m)}[/TEX] the reason I'm interested about the properties of m for this intersection is because as I've stated a few times I saw that if you let [TEX]B = 24\times {A002450}+7[/TEX] [TEX]B = {A083420(n)}[/TEX] for [TEX]{n}\gt 1[/TEX]. So if you prove the properties of the m needed to create set A you can eliminate members of A002450 and hence members of A083420 I know the ones that point to odd composite exponents can be eliminated already but I'm trying to use this to eliminate prime exponents. also these work for all sequences with equations of the form 6*4^n + A000225(2n+1) so I see ways we can use a non infinite subset of A002450 (I'd suggest the lowest values possible).

[QUOTE=science_man_88;248820]I first asked about for what m works such that [TEX] A = {A000040} \cap {A135659(m)}[/TEX][/QUOTE]

What does "works" mean here?

What is A000040 ∩ A135659(m)? This is the intersection of a set and a number. Did you mean A000040 ∩ A135659 = A107006, primes of the form 24n + 7?

[QUOTE=science_man_88;248820]I saw that if you let [TEX]B = 24\times {A002450}+7[/TEX] [TEX]B = {A083420(n)}[/TEX] for [TEX]{n}\gt 1[/TEX].[/QUOTE]

You're saying that 24*A002450(n) + 7 = A083420(n+1), that is, 24 * (4^n - 1)/3 + 7 = 2 * 4^(n+1) - 1. Right?

[QUOTE=science_man_88;248820]So if you prove the properties of the m needed to create set A you can eliminate members of A002450 and hence members of A083420[/QUOTE]

Translation: If you can find an n such that A002450(n) = m such that 24m + 7 is prime, you know that A083420(n+1) is prime. Right?

[QUOTE=science_man_88;248820]I know the ones that point to odd composite exponents can be eliminated already but I'm trying to use this to eliminate prime exponents. also these work for all sequences with equations of the form 6*4^n + A000225(2n+1) so I see ways we can use a non infinite subset of A002450 (I'd suggest the lowest values possible).[/QUOTE]

I trust from reading many of your earlier posts that by "eliminate" you mean find k such that 2^k - 1 is composite. Or do you mean some other exponential sequence, or something else altogether?

[QUOTE=CRGreathouse;248844]What does "works" mean here?

What is A000040 ∩ A135659(m)? This is the intersection of a set and a number. Did you mean A000040 ∩ A135659 = A107006, primes of the form 24n + 7?



You're saying that 24*A002450(n) + 7 = A083420(n+1), that is, 24 * (4^n - 1)/3 + 7 = 2 * 4^(n+1) - 1. Right?



Translation: If you can find an n such that A002450(n) = m such that 24m + 7 is prime, you know that A083420(n+1) is prime. Right?



I trust from reading many of your earlier posts that by "eliminate" you mean find k such that 2^k - 1 is composite. Or do you mean some other exponential sequence, or something else altogether?[/QUOTE]

works here means that if plugging in m proves the intersection true then m is in A, which would be the m such that 24m+7 is prime. well A002450 also appears to fit a(n)= 4*a(n-1)+1 and I've checked this before. For the last 2 you are spot on ( assuming that A083420 is also equal to the odd indexed Mersenne numbers as defined in A000225). This must be a first me understood using symbols and words I've barely learned.

[QUOTE=science_man_88;248845]works here means that if plugging in m proves the intersection true then m is in A, which would be the m such that 24m+7 is prime.[/QUOTE]

"plugging in m proves the intersection true then m is in A" = nonsense. "m such that 24m+7 is prime" is perfect, just what a mathematician would say.

Intersections aren't true or false, sets can't be intersected with numbers (perhaps you meant to intersect with the singleton {A135659(m)}?), etc.

[QUOTE=science_man_88;248845]well A002450 also appears to fit a(n)= 4*a(n-1)+1 and I've checked this before.[/QUOTE]

Right, it's a linear recurrence relation. That particular recurrence is inhomogeneous, but can be transformed into the homogeneous linear recurrence relation a(n) = 5a(n-1) - 4a(n-2).

[QUOTE=science_man_88;248845]For the last 2 you are spot on ( assuming that A083420 is also equal to the odd indexed Mersenne numbers as defined in A000225). This must be a first me understood using symbols and words I've barely learned.[/QUOTE]

If you're able to use your mathematical language correctly (whether in symbols or words) you'll have a much better chance of having your questions understood and answered.

[QUOTE=davar55;247504]Sinve RDS apparently has davar55 on his ignore list,
while davar55 definitely is not igmoring RDS (Dr. Silverman),
can I just say he's welcome to prove his worth any and
every time he chooses. And I know he's human, I meant
only that his attitude toward others is too arrogantly
intolerant. I've found his contributions important
(Sylow Theorems from group theory of basic algebra, idoneal
numbers of Euler, etc etc etc). but his insulting demeanor
irks some of you and makes him difficult to communicate with.[/QUOTE]

Why do you refer to yourself in the 3rd person? I've seen this several times now. Do you not think highly enough of yourself to say "I" or "me"?

Just curious...

[QUOTE=CRGreathouse;248849]"plugging in m proves the intersection true then m is in A" = nonsense. "m such that 24m+7 is prime" is perfect, just what a mathematician would say.

[B]Intersections aren't true or false, sets can't be intersected with numbers (perhaps you meant to intersect with the singleton {A135659(m)}?), etc.[/B]



Right, it's a linear recurrence relation. That particular recurrence is inhomogeneous, but can be transformed into the homogeneous linear recurrence relation a(n) = 5a(n-1) - 4a(n-2).



If you're able to use your mathematical language correctly (whether in symbols or words) you'll have a much better chance of having your questions understood and answered.[/QUOTE]

well basically I want element m to be in A [TEX] A = {A000040} \cap {A135659}[/TEX]

[QUOTE=science_man_88;248922]well basically I want element m to be in A [TEX] A = {A000040} \cap {A135659}[/TEX][/QUOTE]

You can express that as
[TEX]m\in \text{A000040} \cap \text{A135659}[/TEX]
that is, m is an element of the intersection.

[QUOTE=CRGreathouse;248931]You can express that as
[TEX]m\in \text{A000040} \cap \text{A135659}[/TEX]
that is, m is an element of the intersection.[/QUOTE]

I figured I was missing something simple.

does the method check out properly ?

[QUOTE=science_man_88;248937]does the method check out properly ?[/QUOTE]

Would you spell out what you mean by "the method"?

[QUOTE=CRGreathouse;248945]Would you spell out what you mean by "the method"?[/QUOTE]

using the equations I have is it possible to find mersenne primes? The problem for me is speeding this up, as I know it's very slow.

[QUOTE=science_man_88;248946]using the equations I have is it possible to find mersenne primes?[/QUOTE]

Yes, that's the part I want you to be more specific about.

For all[TEX]m\in \text{A000040} \cap \text{A135659}[/TEX] that also fit [TEX]m\in \text{A139483} \cap \text{A002450}[/TEX] and if [TEX]m = \text{A002450(n)}
[/TEX] for some n we can show that A083420(n+1) is prime I can extend this to other sequences of form [TEX]6*4^n + \text{A083420(n-1)}[/TEX] assuming numbering n starts at 0.

[QUOTE=science_man_88;248959]For all [COLOR="Red"]indexes of A135659[/COLOR][TEX]m\in \text{A000040} \cap \text{A135659}[/TEX] that also fit [TEX]m\in \text{A139483} \cap \text{A002450}[/TEX] and if [TEX]m = \text{A002450(n)}
[/TEX] for some n we can show that A083420(n+1) is prime I can extend this to other sequences of form [TEX]6*4^n + \text{A083420(n-1)}[/TEX] assuming numbering n starts at 0.[/QUOTE]

added sorry I'm not thinking today.

[QUOTE=science_man_88;248959]For all[TEX]m\in \text{A000040} \cap \text{A135659}[/TEX] that also fit [TEX]m\in \text{A139483} \cap \text{A002450}[/TEX] and if [TEX]m = \text{A002450(n)}
[/TEX] for some n we can show that A083420(n+1) is prime I can extend this to other sequences of form [TEX]6*4^n + \text{A083420(n-1)}[/TEX] assuming numbering n starts at 0.[/QUOTE]

So if you have a number that, when multiplied by 24 and added to 7, yields a prime, then that number, multiplied by 24 and added to 7, is prime.

[QUOTE=CRGreathouse;249077]So if you have a number that, when multiplied by 24 and added to 7, yields a prime, then that number, multiplied by 24 and added to 7, is prime.[/QUOTE]

not the only thing in there. I know that it's been proven the 24m+7 fits all Mersenne primes >7 so if that m is in A002450 and has index n then A083420(n+1) is prime.

[QUOTE=science_man_88;249084]if that m is in A002450 and has index n then A083420(n+1) is prime.[/QUOTE]

Let's work through this. If m = A002450(n) then we have m = (4[SUP]n[/SUP] - 1)/3. That means 3m = 4[SUP]n[/SUP] - 1 and so 3m + 1 = 4[SUP]n[/SUP]. Taking the base-4 log we get log(3m + 1) = n. Substituting this into the formula for A083420 we have
2 * 4[SUP]log(3m + 1) + 1[/SUP] - 1. Pulling a 1 out of the exponent we get 8 * 4[SUP]log(3m + 1)[/SUP] - 1. Since '4 to the power' and 'base-4 log' are inverses, we get 8 * (3m + 1) - 1. Simplifying, this is 24m + 7.

So yes, that's all this is. You're not using properties like the form of Mersenne numbers, you're just saying that 24m + 7 is prime iff 24m + 7 is prime.

[QUOTE=CRGreathouse;249087]Let's work through this. If m = A002450(n) then we have m = (4[SUP]n[/SUP] - 1)/3. That means 3m = 4[SUP]n[/SUP] - 1 and so 3m + 1 = 4[SUP]n[/SUP]. Taking the base-4 log we get log(3m + 1) = n. Substituting this into the formula for A083420 we have
2 * 4[SUP]log(3m + 1) + 1[/SUP] - 1. Pulling a 1 out of the exponent we get 8 * 4[SUP]log(3m + 1)[/SUP] - 1. Since '4 to the power' and 'base-4 log' are inverses, we get 8 * (3m + 1) - 1. Simplifying, this is 24m + 7.

So yes, that's all this is. You're not using properties like the form of Mersenne numbers, you're just saying that 24m + 7 is prime iff 24m + 7 is prime.[/QUOTE]

how it links to mersenne numbers is that 24(A002450) + 7 = a odd indexed mersenne number.

[QUOTE=science_man_88;249088]how it links to mersenne numbers is that 24(A002450) + 7 = a odd indexed mersenne number.[/QUOTE]

Yes. So if you have a prime Mersenne number you know that it is prime.

[QUOTE=CRGreathouse;249093]Yes. So if you have a prime Mersenne number you know that it is prime.[/QUOTE]

not quite what I was going for. I was more heading towards if we can use properties of m such that 24m+7 is prime we can check to see which m in 2450 have the properties needed to make 24m+7 prime and hence in this case [COLOR="Red"]be[/COLOR] [COLOR="Lime"]create[/COLOR] a Mersenne prime.

Wow.. There hasn't been much going on in the time that I've disappeared..

Some things never change..

[QUOTE=gd_barnes;248906]Why do you refer to yourself in the 3rd person? I've seen this several times now. Do you not think highly enough of yourself to say "I" or "me"?

Just curious...[/QUOTE]

I (meaning me) refer to myself as davar55 in this way in this forum
only in certain contexts. In that post, since I referred to Dr.Silverman
by the initials RDS, I used davar55 to refer to me, rather than me or I.

Just courtesy.

Don't forget that the elements of oeis are sequences, not sets.

Sequences are ordered and can have repeated values.
Sets are unordered and (in normal representation) non-repeated.

For sets of integers BTW an ordered representation is
"standard normal form".

Bob's lack of attention?
 

[QUOTE=R.D. Silverman;247041]24m+7 can be prime if m != 0 mod 7[/QUOTE]

To get this back to the actual topic, I would like to point out the fallacies of Robert Silverman's above quoted formula. This statement is, in and of itself, false. If m!=0 mod 7, then m MUST be greater than or equal to 7. This is not a requirement, but merely a poor musing that put no thought into the question. 24(1)+7=31
24(3)+7=79
24(4)+7=103
24(5)+7=127
24(6)+7=151
((24(7)+7=175)) though 7!=0 mod 7
24(8)+7=199
This does not appear to be a modular function in terms of m, but I very likely could be wrong.

Just to CMA, if Mr. Silverman was attempting to be clever, I apologize for my inability to acknowledge his sarcasm, particularly after being followed by abashment of a peer. However, he will be reminded that what we lack in mathematical knowledge initially, we make up for in technology and willingness to learn.

That is all.

[QUOTE=c10ck3r;257336]To get this back to the actual topic, I would like to point out the fallacies of Robert Silverman's above quoted formula. This statement is, in and of itself, false. If m!=0 mod 7, then m MUST be greater than or equal to 7.
[/QUOTE]

Huh???. m = 1,2,3,4,5, or 6 are not 0 mod 7, yet m < 7. Surely, this
can't be what you meant?

m!= 0 mod 7 is a necessary condition for 24m+7 to be prime except for the
special (degenerate case) m = 0. Otherwise 24m+7 will be divisible by 7.
I believe that m > 0 was part of the conditions.


[QUOTE]

This is not a requirement, but merely a poor musing that put no thought into the question. 24(1)+7=31
24(3)+7=79
24(4)+7=103
24(5)+7=127
24(6)+7=151
((24(7)+7=175)) though 7!=0 mod 7

[/QUOTE]

Complete idiot. 7 certainly does equal 0 mod 7.

[QUOTE]
24(8)+7=199
This does not appear to be a modular function in terms of m, but I very likely could be wrong.
[/QUOTE]

You have ZERO idea of what a modular function is. Try google. I will
give some hints:

(1) It is a meromorphic function in the upper half plane.
(yes, I know. You are lost already)
(2) The function involves the modular group; an instance of
SL(2,Z) (still lost......)
(3) Do you know what a linear fractional transformation is?

[QUOTE=R.D. Silverman;257341]Huh???. m = 1,2,3,4,5, or 6 are not 0 mod 7, yet m < 7. Surely, this
can't be what you meant?

m!= 0 mod 7 is a necessary condition for 24m+7 to be prime except for the
special (degenerate case) m = 0. Otherwise 24m+7 will be divisible by 7.
I believe that m > 0 was part of the conditions.




Complete idiot. 7 certainly does equal 0 mod 7.



You have ZERO idea of what a modular function is. Try google. I will
give some hints:

(1) It is a meromorphic function in the upper half plane.
(yes, I know. You are lost already)
(2) The function involves the modular group; an instance of
SL(2,Z) (still lost......)
(3) Do you know what a linear fractional transformation is?[/QUOTE]

Here's an exercize for you.

Prove (or disprove) that a linear fractional transform under the modular
group is a conformal map of the upper half plane.

[QUOTE=R.D. Silverman;257343]Here's an exercize for you.

Prove (or disprove) that a linear fractional transform under the modular
group is a conformal map of the upper half plane.[/QUOTE]

and easier way would be that z=x mod y shows that z|y with remainder x. and then go on to show 7|7 with remainder 0.

[QUOTE=R.D. Silverman;257341]Huh???. m = 1,2,3,4,5, or 6 are not 0 mod 7, yet m < 7. Surely, this
can't be what you meant?

m!= 0 mod 7 is a necessary condition for 24m+7 to be prime except for the
special (degenerate case) m = 0. Otherwise 24m+7 will be divisible by 7.
I believe that m > 0 was part of the conditions.


Complete idiot. 7 certainly does equal 0 mod 7.

[/QUOTE]

Ah, yet you still miss what I was trying to say. The statement I was making to clarify other possibilities beyond m!=0 mod 7. When m=1, m!=1 mod 7, and 24m+7 IS prime. When m=3, m!=6 mod 7, and 24m+7 IS prime. What I was attempting to point out is that m! does not, but may, equal 0 mod 7 for 24m+7 to be prime. Also, m!=0 mod 7 for all m's greater than or equal to 7. You will note that 8!=40320, which is 0 mod 7, as is 9!, 10!, 11!, et al. Yes, et al. Taking n>x, n!=0 mod x, where both are whole numbers.

The "necessary condition" is that m is not a multiple of 7. If m IS a multiple of 7 (we'll use 77 as a generic example), then 24m+7 is evenly divisible by 7.
See first year college algebra for the logic used. 24*77+7=1855, which is 5*[B]7[/B]*53.

This is not a requirement, but merely a poor musing that put no thought into the question. 24(1)+7=31
24(3)+7=79
24(4)+7=103
24(5)+7=127
24(6)+7=151
((24(7)+7=175)) though 7!=0 mod 7

when m=1,3,4,5, or 6, m! does not equal 0 mod 7, yet the result is prime. However, when 7 is used for m, m!=0 mod 7 as you earlier stated as a requirement, but does not make the equation prime.

[QUOTE=c10ck3r;257386]This is not a requirement, but merely a poor musing that put no thought into the question. 24(1)+7=31
24(3)+7=79
24(4)+7=103
24(5)+7=127
24(6)+7=151
((24(7)+7=175)) though 7!=0 mod 7

when m=1,3,4,5, or 6, m! does not equal 0 mod 7, yet the result is prime. However, when 7 is used for m, m!=0 mod 7 as you earlier stated as a requirement, but does not make the equation prime.[/QUOTE]

!= means "not equal" in programming not "factorial equal". A easy way to remember this is "! =" is "factorial equals" and "!=" is "not equal""

[QUOTE=c10ck3r;257385]Ah, yet you still miss what I was trying to say. The statement I was making to clarify other possibilities beyond m!=0 mod 7. When m=1, m!=1 mod 7, and 24m+7 IS prime.

[/QUOTE]

Duh! m = 1 mod 7 means that m!= 0 mod 7.

Look, moron. There are only two possibilities. Either m = 0 mod 7,
in which case 24m+7 is prime only for m = 0, or m != 0 mod 7, in which
case 24m + 7 can be prime.

[QUOTE]
When m=3, m!=6 mod 7, and 24m+7 IS prime. What I was attempting to point out is that m! does not, but may, equal 0 mod 7 for 24m+7 to be prime.
[/QUOTE]

Digging yourself deeper and deeper. if m = 0 mod 7, then m = 7K
whence 24(7K) + 7 is divisible by 7 and hence NOT prime except for
7 itself (m = 0)

<plonk>

You are a total cretin and don't even realize it.

[QUOTE]
Also, m!=0 mod 7 for all m's greater than or equal to 7.
[/QUOTE]

Another idiotic statement. m = 14 is certainly greater than 7 and is
certainly 0 mod 7.

[QUOTE=R.D. Silverman;257401]Duh! m = 1 mod 7 means that m!= 0 mod 7.

Look, moron. There are only two possibilities. Either m = 0 mod 7,
in which case 24m+7 is prime only for m = 0, or m != 0 mod 7, in which
case 24m + 7 can be prime.



Digging yourself deeper and deeper. if m = 0 mod 7, then m = 7K
whence 24(7K) + 7 is divisible by 7 and hence NOT prime except for
7 itself (m = 0)

<plonk>

You are a total cretin and don't even realize it.



Another idiotic statement. m = 14 is certainly greater than 7 and is
certainly 0 mod 7.[/QUOTE]

I think what's going on is that they are mistaking m is not equal to 0 mod 7 for m factorial is equal to 0 mod 7. I get this from:

[QUOTE=c10ck3r;257385] 8!=40320[/QUOTE]

8 factorial is equal to 40320 so they are thinking the ! is factorial when it's the programming for not.

Bob-I apologize for the misunderstanding. However, on a MATH forum, one would expect symbols to take their math definitions and not code form. Next time, please clarify by using mathematics in math forums, even if only in brackets. In case you were unaware, it is unicode 2260. Sorry for the confusion.

[QUOTE=c10ck3r;258322]Bob-I apologize for the misunderstanding. However, on a MATH forum, one would expect symbols to take their math definitions and not code form. Next time, please clarify by using mathematics in math forums, even if only in brackets. In case you were unaware, it is unicode 2260. Sorry for the confusion.[/QUOTE]

it's not just a math forum though it's got a programming section in the main forums. Anyways I caught the difference just took me a while. The main problem i had was as described x"! =" is likely factorial, x!= you can't tell without doing math, and x" !=", is x is not equal to.

[QUOTE=science_man_88;258335]it's not just a math forum though it's got a programming section in the main forums. Anyways I caught the difference just took me a while. The main problem i had was as described x"! =" is likely factorial, x!= you can't tell without doing math, and x" !=", is x is not equal to.[/QUOTE]

of course x! = and [TEX]\ne[/TEX] solves such arguments.