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-   -   "New" primality test/check (https://www.mersenneforum.org/showthread.php?t=22838)

gophne 2017-12-31 02:38

Hi Batalov

I love Jim Carrey, but are we not getting distracted?

chalsall 2017-12-31 02:40

[QUOTE=gophne;475516]OR in this case x==y versus x==y mod x.[/QUOTE]

What about x==y vs. x!=y?

gophne 2017-12-31 02:41

[QUOTE=chalsall;475515]Hi gophne. With all due respect, I wasn't name calling, nor meaning to insult.

The referral to monkeys and typewriters and Shakespeare is a very common reference in statistics.

You have, of course, read the prior art.

I apologise if I manage to insult you, or anyone.[/QUOTE]
Hi chalsall

Apology excepted. I have a very thick skin! :)

gophne 2017-12-31 02:43

[QUOTE=chalsall;475518]What about x==y vs. x!=y?[/QUOTE]
Hi chalsall

I don't get you...the two statements are clearly different...was this a typo?

chalsall 2017-12-31 02:46

[QUOTE=gophne;475520]I don't get you...[/QUOTE]

That doesn't surprise me at all.

gophne 2017-12-31 03:07

[QUOTE=CRGreathouse;475501]Rediscovery is commonplace, and not a problem. All of us have rediscovered existing theorems, algorithms, or the like at some point. The trouble in your case isn’t that you rediscovered Fermat’s test, but that you claimed that it was a primality test (no exceptions) rather than a probable-prime test.[/QUOTE]
Hi CRGreathouse

I had a look at the post by ewmayer again after the tread was reopened. For me they are similar but not the same...big difference.

I think ewmayer might unwittingly have slightly tweaked my algorithm as posted.

I would think that a simle and difinitive way to confirm the equivalance or otherwise would be to substitute values into the formulas...if the give the same exact result...they are the same....if they give different results, the formulas/algorithms are different.

I claimed that the algorthm I had posted determines [I]primality and compositeness[/I] (albeit with false positives which is not unique with primality algorithms), [I]not[/I] that it was a pseudo-prime/false prime test.

[B]ewmayer[/B] suggested that "my" algorithm might or is likely a copy of an existing pseudo-prime checker (which I am willing to accept), but simple substitution with values does not support the statement that the two algorithms are the same.

Regards

chalsall 2017-12-31 03:18

[QUOTE=gophne;475526]I think ewmayer might unwittingly have slightly tweaked my algorithm as posted.[/QUOTE]

No difference. It was a simple symbolic algebra reduction which you should have been taught in high school.

If you weren't, that's your problem, not ours.

CRGreathouse 2017-12-31 05:58

[QUOTE=gophne;475526]I claimed that the algorthm I had posted determines [I]primality and compositeness[/I] (albeit with false positives which is not unique with primality algorithms), [I]not[/I] that it was a pseudo-prime/false prime test.[/QUOTE]

You seem to be confused as to the definitions of those terms.

xilman 2017-12-31 11:55

[QUOTE=Batalov;475464]I wrote a ground-breaking new poem and I shall go around telling everyone that I've truly made something out of myself. Here is small bit of it. I have more, much more! --
[QUOTE]To be, or not to be--that is the question:
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune
Or to take arms against a sea of troubles[/quote]
Now some people keep telling me that some guy with a spear (never heard of him) already wrote something similar. But it is false. Mine is completely different. His version has some extra commas and the words are not the same; first of all, they are completely unnecessary, and secondly, surely this makes it not the same.[/QUOTE]
I like my take on the great speech more than yours. It goes:

To be, or not to be -- that is what we must ask:
If it is more good in the mind to bear the
The slings and darts of sheer bad luck
Or take up arms to a sea of woes.
And through a fight back, end them. To die, to sleep --
No more -- and by a sleep to say we end
The heart's ache, and the ten times ten times ten real shocks
That flesh is heir to. 'Tis an end
Much to be wished. To die, to sleep --
To sleep -- a chance to dream: ay, there's the rub,
For in that sleep of death what dreams may come
When we have left this life,
Must give us pause. There's the thing
That makes a curse of so long life.
For who would bear the whips and scorns of time.

guptadeva 2017-12-31 12:08

[QUOTE=xilman;475561]I like my take on the great speech more than yours. It goes:

To be, or not to be -- that is what we must ask:
If it is more good in the mind to bear the
The slings and darts of sheer bad luck
Or take up arms to a sea of woes.
And through a fight back, end them. To die, to sleep --
No more -- and by a sleep to say we end
The heart's ache, and the ten times ten times ten real shocks
That flesh is heir to. 'Tis an end
Much to be wished. To die, to sleep --
To sleep -- a chance to dream: ay, there's the rub,
For in that sleep of death what dreams may come
When we have left this life,
Must give us pause. There's the thing
That makes a curse of so long life.
For who would bear the whips and scorns of time.[/QUOTE]

great ... also your "ten times ten times ten" is a very appropriate opportunity to emphasize the pain of hamlet :lol:

for completeness - here's the original quote:

[QUOTE][I]To be, or not to be: that is the question:
Whether ’tis nobler in the mind to suffer
The slings and arrows of outrageous fortune,
Or to take arms against a sea of troubles,
And by opposing end them? To die: to sleep;
No more; and by a sleep to say we end
The heart-ache and the thousand natural shocks
That flesh is heir to, ’tis a consummation
Devoutly to be wish’d. To die, to sleep;
To sleep: perchance to dream: ay, there’s the rub;
For in that sleep of death what dreams may come
When we have shuffled off this mortal coil,
Must give us pause: there’s the respect
That makes calamity of so long life;
For who would bear the whips and scorns of time,
The oppressor’s wrong, the proud man’s contumely,
The pangs of despised love, the law’s delay,
The insolence of office and the spurns
That patient merit of the unworthy takes,
When he himself might his quietus make
With a bare bodkin? who would fardels bear,
To grunt and sweat under a weary life,
But that the dread of something after death,
The undiscover’d country from whose bourn
No traveller returns, puzzles the will
And makes us rather bear those ills we have
Than fly to others that we know not of?
Thus conscience does make cowards of us all;
And thus the native hue of resolution
Is sicklied o’er with the pale cast of thought,
And enterprises of great pith and moment
With this regard their currents turn awry,
And lose the name of action.–Soft you now!
The fair Ophelia! Nymph, in thy orisons
Be all my sins remember’d.[/I][/QUOTE]

gophne 2017-12-31 16:19

[QUOTE=chalsall;475529]No difference. It was a simple symbolic algebra reduction which you should have been taught in high school.

If you weren't, that's your problem, not ours.[/QUOTE]
Hi chalsall

I cannot understand the underlying agression of the senior contributors on this site towards me and I suppose my submissions. To me it seems reminiscent of the suppression of ideas in the Dark Ages actually. I cannot understand the hostility on such a reputable site such as the mersenneforum.

What is more baffling is that evrybody sems to be flinging accusations and comments around and none is doing the math.

IF the algorithms are the same (not what ewmayer or any other contributer might say), the only way is the math/science way...DO THE MATH. COMPARE. POST THE FINDINGS....NOT COMMENTS.

That I believe would be what other interested contributors would appreciate.

Thanx

science_man_88 2017-12-31 16:24

[QUOTE=gophne;475589]Hi chalsall

I cannot understand the underlying agression of the senior contributors on this site towards me and I suppose my submissions. To me it seems reminiscent of the suppression of ideas in the Dark Ages actually. I cannot understand the hostility on such a reputable site such as the mersenneforum.

What is more baffling is that evrybody sems to be flinging accusations and comments around and none is doing the math.

IF the algorithms are the same (not what ewmayer or any other contributer might say), the only way is the math/science way...DO THE MATH. COMPARE. POST THE FINDINGS....NOT COMMENTS.

That I believe would be what other interested contributors would appreciate.

Thanx[/QUOTE]

The math has been shown already. I like to play around more than most here.

gophne 2017-12-31 16:29

[QUOTE=CRGreathouse;475542]You seem to be confused as to the definitions of those terms.[/QUOTE]
Hi CRGreathouse

I might be confused, but still I am only getting comments on the issue/comparisons. That is neither here nor there. I know that you are a very senior, knowledgable and respected person on this Site (possibly a Professor at some University as well I think). Could you please run the two algorithms, the one I posted (on gophne thread #73 I think) and the one that awmayer "reduced" a bit further on in the thread. If you could that present to all your results. If the two algorithms gives the same result/s then I will accept that the two algorithms are indeed the same.

Perhaps if you could also advise what the name/source of the algorithm that ewmayer has reduced to...he did not state this in his post...I have taken it on trust that such analgorithm exists.

Thanx so much.

gophne 2017-12-31 16:36

[QUOTE=science_man_88;475590]The math has been shown already. I like to play around more than most here.[/QUOTE]
MORE COMMENTS....PLEASE STATE THE MATH FOR THOSE THAT MIGHT HAVE MISSED IT.

If the algorithms are the same...substitute values into the formulas and report what comes out ! Please!

I think everybody is crying out for this. May I suggest that you start with the number 1 or any other number that tickles your fancy.

That is what we did at primary school be entering numbers into little squares to make the answer true.

For Pete's sake.

science_man_88 2017-12-31 16:45

It's literally a transform of n+2---------->n in you formula and then a reworking it.

Batalov 2017-12-31 16:56

1 Attachment(s)
[QUOTE=gophne;475598]MORE COMMENTS....

...That is what we did at primary school be entering numbers into little squares to make the answer true.

For Pete's sake.[/QUOTE]
Suppose you wanted to learn the piano and transposed the Moonlight sonata into a more convenient key (from the original c# minor ...that, obviously everyone knows :rolleys:). You cannot go around claiming that you wrote new music.

Suppose you don't understand sheet music at all. Don't expect us to explain it after 3- 4 attempts as you clearly need a music teacher and study for >5 years to play this --

ATH 2017-12-31 17:03

[QUOTE=gophne;475598]MORE COMMENTS....PLEASE STATE THE MATH FOR THOSE THAT MIGHT HAVE MISSED IT.[/QUOTE]

It was you that missed the math or rather you did not understand.

We claim your algorithm is the fermat pseudoprime test to base 2, so test your algorithm on numbers up to say 10,000. We claim it will find the real primes as well as these composite numbers as "false positives":

[url]http://oeis.org/A001567[/url]
341, 561, 645, 1105, 1387, 1729, 1905, 2047, 2465, 2701, 2821, 3277, 4033, 4369, 4371, 4681, 5461, 6601, 7957, 8321, 8481, 8911

Here are the list of real primes if you need it:
[url]https://primes.utm.edu/lists/small/10000.txt[/url]

science_man_88 2017-12-31 17:25

A bit more explicit.


2^n-1 == (n+1)/2 mod (n+2)
2^((n+2)-2)-1== ((n+2)-1)/2 mod (n+2)
Replacing n+2 with n we get:
2^(n-2)-1==(n-1)/2 mod n
2^(n-1)-2==n-1 mod n
2^(n-1)== n+1 mod n

Casting out the terms that don't affect the remainder we get.

2^(n-1)==1 mod n QED edit if this doesn't register you need to brush up on mathematical laws like the law of replacement, or you need to look up what modular arithmetic is.

guptadeva 2017-12-31 17:55

1 Attachment(s)
[QUOTE=gophne;475598]
If the algorithms are the same...substitute values into the formulas and report what comes out ! Please!
[/QUOTE]

the algorithms are the same just take a look for yourself:

[ATTACH]17438[/ATTACH]

on the left side (in red) are the numbers from "your" algorithm and on the right side (in green) are the numbers from fermat

it really does not matter what the exact numbers are therein ... only the fact, that all the numbers that are equal on the left side correspond to some other numbers that are equal on the right side is important here !

can you see, that all the equal signs are in the same positions in both algorithms ?
now, the tables are only having 14 lines each but do you think, that the equal signs would always be in the same positions if both tables had 100 lines or even 1000 lines ?

you are welcome to make the calculations yourself and you will see that the equal signs [U]always[/U] stay in the same positions ?

how do we know this without actually having made such huge tables ?

well, we use modular math - you should really take your time and learn what this mod function is all about:

the "rules" for the mod-function do not equal to the rules of the normal equal sign
so you might take a look on

[URL]https://en.wikipedia.org/wiki/Modular_arithmetic[/URL]

or other pages on the internet to learn what these "rules" are ... and also more important to truely understand WHY they are in that way they are.

the "experts" on this forum have spent quite a long time to practice and finally truely understand this WHY

this is the reason for their statement that the two algorithms are exactly the same ...

using the mod-function is as simple and easy as playing the moonlight sonata on piano for them

gophne 2017-12-31 18:35

[QUOTE=science_man_88;475603]It's literally a transform of n+2---------->n in you formula and then a reworking it.[/QUOTE]
Hi science_man_88

Please run the algorithms and POST the results. I do not have X-ray eyes ;)

gophne 2017-12-31 18:39

[QUOTE=Batalov;475607]Suppose you wanted to learn the piano and transposed the Moonlight sonata into a more convenient key (from the original c# minor ...that, obviously everyone knows :rolleys:). You cannot go around claiming that you wrote new music.

Suppose you don't understand sheet music at all. Don't expect us to explain it after 3- 4 attempts as you clearly need a music teacher and study for >5 years to play this --[/QUOTE]
Hi Batalov

Regretfully commentary would not suffice as proof of the identity of the algorithms under the spotlight.

By the way, do you know what the algorithm /formula is that [B]awmayer[/B] was reducing to? What is his source or the name of this formula/algorithm?

gophne 2017-12-31 18:46

[QUOTE=guptadeva;475614]the algorithms are the same just take a look for yourself:

[ATTACH]17438[/ATTACH]

on the left side (in red) are the numbers from "your" algorithm and on the right side (in green) are the numbers from fermat

it really does not matter what the exact numbers are therein ... only the fact, that all the numbers that are equal on the left side correspond to some other numbers that are equal on the right side is important here !

can you see, that all the equal signs are in the same positions in both algorithms ?
now, the tables are only having 14 lines each but do you think, that the equal signs would always be in the same positions if both tables had 100 lines or even 1000 lines ?

you are welcome to make the calculations yourself and you will see that the equal signs [U]always[/U] stay in the same positions ?

how do we know this without actually having made such huge tables ?

well, we use modular math - you should really take your time and learn what this mod function is all about:

the "rules" for the mod-function do not equal to the rules of the normal equal sign
so you might take a look on

[URL]https://en.wikipedia.org/wiki/Modular_arithmetic[/URL]

or other pages on the internet to learn what these "rules" are ... and also more important to truely understand WHY they are in that way they are.

the "experts" on this forum have spent quite a long time to practice and finally truely understand this WHY

this is the reason for their statement that the two algorithms are exactly the same ...

using the mod-function is as simple and easy as playing the moonlight sonata on piano for them[/QUOTE]
Hi guptadeva

This is more in line with what we need. From what you say indications are that the two algorithms are the same.

However, I cannot make out anything on the image you posted, could you perhaps tabulate the results and the algorithms that generated them (as well as the inputs).

Thanx, Regards.

gophne 2017-12-31 18:57

[QUOTE=ATH;475608]It was you that missed the math or rather you did not understand.

We claim your algorithm is the fermat pseudoprime test to base 2, so test your algorithm on numbers up to say 10,000. We claim it will find the real primes as well as these composite numbers as "false positives":

[url]http://oeis.org/A001567[/url]
341, 561, 645, 1105, 1387, 1729, 1905, 2047, 2465, 2701, 2821, 3277, 4033, 4369, 4371, 4681, 5461, 6601, 7957, 8321, 8481, 8911

Here are the list of real primes if you need it:
[url]https://primes.utm.edu/lists/small/10000.txt[/url][/QUOTE]
Hi ATH

Thanx for indicating the numbers that are the same. Can you give us the EXACT breakdown that each of the Algorithms generate as well please, for the record or at least say the first 30 terms of each.

Regards

gophne 2017-12-31 19:05

[QUOTE=science_man_88;475610]A bit more explicit.


2^n-1 == (n+1)/2 mod (n+2)
2^((n+2)-2)-1== ((n+2)-1)/2 mod (n+2)
Replacing n+2 with n we get:
2^(n-2)-1==(n-1)/2 mod n
2^(n-1)-2==n-1 mod n
2^(n-1)== n+1 mod n

Casting out the terms that don't affect the remainder we get.

2^(n-1)==1 mod n QED edit if this doesn't register you need to brush up on mathematical laws like the law of replacement, or you need to look up what modular arithmetic is.[/QUOTE]
Hi science_man_88

Your math is incorrect;

LHS of == sign

2^n-1....let n=5

Then LHS result is 31

RHS of == sign

(n+1)/2 mod (n+2).......substitute for n=5

(5+1)/2 mod (5+2)

RHS result is =3

10metreh 2017-12-31 19:25

[QUOTE=gophne;475627]Hi science_man_88

Your math is incorrect;

LHS of == sign

2^n-1....let n=5

Then LHS result is 31

RHS of == sign

(n+1)/2 mod (n+2).......substitute for n=5

(5+1)/2 mod (5+2)

RHS result is =3[/QUOTE]

"mod" isn't an operator. You can't just apply it to one side of an equation. It isn't the same as the "%" operator in many programming languages, though it is somewhat similar.

When we say that a ≡ b (mod n), what we mean is that n divides a-b exactly (or, equivalently, that a and b leave the same remainder on division by n). So, for example, 1 ≡ 11 (mod 5), because 5 divides 1-11 = -10 exactly.

When n=5, indeed 2^n-1 = 31 and (n+1)/2 = 3.
These are not equal, but 2^n-1 ≡ (n+1)/2 (mod n+2) is still true, because 7 divides 31-3 = 28 exactly, and 31 ≡ 3 (mod 7).

The "%" operator gives the remainder you get when you divide one number by another.
Note that if b = a%n, then a = kn+b for some integer k: that's what we mean by a remainder. Then a-b = kn, so a ≡ b (mod n). This is how "mod" and "%" are related.
For positive integers, a ≡ b (mod n) is equivalent to a%n = b%n. (You need to be careful with negative numbers because programming languages may define a%n to have the same sign as a.)

CRGreathouse 2017-12-31 19:36

[QUOTE=gophne;475595]Could you please run the two algorithms, the one I posted (on gophne thread #73 I think) and the one that awmayer "reduced" a bit further on in the thread. If you could that present to all your results. If the two algorithms gives the same result/s then I will accept that the two algorithms are indeed the same.[/QUOTE]

I can’t take on unpaid projects at this time, sorry.

gophne 2017-12-31 19:41

[QUOTE=10metreh;475632]"mod" isn't an operator. You can't just apply it to one side of an equation. It isn't the same as the "%" operator in many programming languages, though it is somewhat similar.

When we say that a ≡ b (mod n), what we mean is that n divides a-b exactly (or, equivalently, that a and b leave the same remainder on division by n). So, for example, 1 ≡ 11 (mod 5), because 5 divides 1-11 = -10 exactly.

When n=5, indeed 2^n-1 = 31 and (n+1)/2 = 3.
These are not equal, but 2^n-1 ≡ (n+1)/2 (mod n+2) is still true, because 7 divides 31-3 = 28 exactly, and 31 ≡ 3 (mod 7).

The "%" operator gives the remainder you get when you divide one number by another.
Note that if b = a%n, then a = kn+b for some integer k: that's what we mean by a remainder. Then a-b = kn, so a ≡ b (mod n). This is how "mod" and "%" are related.
For positive integers, a ≡ b (mod n) is equivalent to a%n = b%n. (You need to be careful with negative numbers because programming languages may define a%n to have the same sign as a.)[/QUOTE]
[B]Hi 10metreh[/B]

No disagreement here: 31 mod 7 ≡ 3

However the logical [B]==[/B] determinant means [B]IS IDENTICAL.[/B] 31[B]<>[/B]3

Consider the following:

x==31 and x==31 mod 7....THEY ARE NOT THE SAME

gophne 2017-12-31 19:45

[QUOTE=CRGreathouse;475636]I can’t take on unpaid projects at this time, sorry.[/QUOTE]
Hi CRGreathouse

You seem to have no problem with gratis comments :)

I know I am dumb, but please help me to understand and stop me from being a nuisance by posting the results for all to see and to analyse the outcomes. Ppl wil have a lot of faith in your results.

CRGreathouse 2017-12-31 20:06

[QUOTE=gophne;475638]You seem to have no problem with gratis comments :)

I know I am dumb, but please help me to understand and stop me from being a nuisance by posting the results for all to see and to analyse the outcomes. Ppl wil have a lot of faith in your results.[/QUOTE]

In fact I may have to cut back the gratis comments to make time for other commitments. But for the moment I can spare a bit of time.

I’ll be happy to carry out the analysis however you like, and write whatever supporting code is needed, as soon as the check clears in my bank account. Until then I recommend further study which will (in addition to enhancing your life) make it easier for you to understand the equivalence. If interested, forum members are usually more than happy to recommend resources.

gophne 2017-12-31 20:35

[QUOTE=CRGreathouse;475647]In fact I may have to cut back the gratis comments to make time for other commitments. But for the moment I can spare a bit of time.

I’ll be happy to carry out the analysis however you like, and write whatever supporting code is needed, as soon as the check clears in my bank account. Until then I recommend further study which will (in addition to enhancing your life) make it easier for you to understand the equivalence. If interested, forum members are usually more than happy to recommend resources.[/QUOTE]
Hi CRGreathouse

I respect that you have other tasks on the Site, it is just that I had thought that if you had done the analysis, that would have been much more authoritative.

When I dream the first 100 million digit mersenne prime, I will hire your services :)

Thanx for interactions and advice.

science_man_88 2017-12-31 20:41

[QUOTE=gophne;475652]Hi CRGreathouse

I respect that you have other tasks on the Site, it is just that I had thought that if you had done the analysis, that would have been much more authoritative.

When I dream the first 100 million digit mersenne prime, I will hire your services :)

Thanx for interactions and advice.[/QUOTE]

Look up proof by authority...

VBCurtis 2017-12-31 22:25

[QUOTE=chalsall;475522]That doesn't surprise me at all.[/QUOTE]

:tu:

George M 2017-12-31 22:39

X!=Y means X does not equal Y.... right?
 
I read the title on a mathematical symbols keyboard. Wait, I am not replying to the right post, am I? If so, then just ignore this.

gophne 2017-12-31 23:00

Hi George M

[B] !=[/B] does mean "[I]not equal to[/I]" in some computer code.

gophne 2018-01-01 06:54

RETRACTION
 
Hi Everybody

I acknowledge that "my" algorithm is a "clone" of Fermat, after the answer to runs of the two algorithms by [B]10metreh, post #22[/B], in the [B]OMG, I cannot spam anymore in the forum Feedback where my question was answered!!!!!!!!!!111111[/B]

[I]The results posted prove conclusively that "my" algorithm is a clone/copy of Fermat's.[/I]

I apologise for not being to graps this earlier. Egg all over my face and many frustrated contributers.

All I can do now is to provide the background work that I had used to derive "my" algorithm, if anybody might be interested. I did not use Fermat.

Oh my gosh!!!

chalsall 2018-01-01 07:20

[QUOTE=gophne;475802]I acknowledge that "my" algorithm is a "clone" of Fermat.[/QUOTE]

If I may please say, you are quite possibly the funniest AI we've ever had here.

[QUOTE=gophne;475802]All I can do now is to provide the background work that I had used to derive "my" algorithm, if anybody might be interested. I did not use Fermat.[/QUOTE]

No need.

Any high-school student worth their salt would have parsed your language, and your maths, in their head.

guptadeva 2018-01-01 10:44

eucleides is said to have replied to king ptolemaios' request for an easy way of learning mathematics: "THERE IS NO ROYAL WAY TO MATHEMATICS"

as an unnknown greek translator once joked, the quote of euclid could also be interpreted as "THERE IS NO WAY MORE ROYAL THAN THE MATHEMATICS"

as far as i know ptolemaios assured eucleides that he would study hard and not make any shortcuts ...

eucleides did in fact teach ptolemaios some simple mathematics as he perfectly understood the future value of this - it had been a longstanding dream of eucleides that a library in alexandria be build - so after having taught ptolemaios to appreciate the value of science, a library was build in alexandria with support from ptolemaios.

also eratosthenes, later working in the library of alexandria as the chief librarian had enough time to sift through the huge ammount of precious scientific works collected there

euceides never taught any geometry to ptolemaios ... but that's another story ...

gophne 2018-01-01 11:42

[QUOTE=chalsall;475808]If I may please say, you are quite possibly the funniest AI we've ever had here.



No need.

Any high-school student worth their salt would have parsed your language, and your maths, in their head.[/QUOTE]
Hi chalsall

You point is taken.

I think you came from your mothers womb already filled with wisdom and magnanimity, because it is shining from you like a fiery beacon.

You are a colossus of a human being....there are and never will be anybody like you that will walk on this earth.

You must enjoy and never forget or let others forget this very special gift that you have been born with.

Go well.

gophne 2018-01-01 12:05

[QUOTE=guptadeva;475816]eucleides is said to have replied to king ptolemaios' request for an easy way of learning mathematics: "THERE IS NO ROYAL WAY TO MATHEMATICS"

as an unnknown greek translator once joked, the quote of euclid could also be interpreted as "THERE IS NO WAY MORE ROYAL THAN THE MATHEMATICS"

as far as i know ptolemaios assured eucleides that he would study hard and not make any shortcuts ...

eucleides did in fact teach ptolemaios some simple mathematics as he perfectly understood the future value of this - it had been a longstanding dream of eucleides that a library in alexandria be build - so after having taught ptolemaios to appreciate the value of science, a library was build in alexandria with support from ptolemaios.

also eratosthenes, later working in the library of alexandria as the chief librarian had enough time to sift through the huge ammount of precious scientific works collected there

euceides never taught any geometry to ptolemaios ... but that's another story ...[/QUOTE]
Thanks.....the embarassment runs deep, but I take heart from your message. I supposed the history of maths is littered with all kinds of wanna-be's like myself. But then again, lots of knowledge must have been born in fits of insanity...unfortunately for me this was not one of those times :(

However, prime search is my hobby....and I will continue to search....and hopefully I will not be pre-judged by this faux pas...there could be many more.

I will post on this thread, once the thunder has passed, the background work from which I derived the formula that I had posted, which was not from Fermat.

Until then I will keep as low a profile as possible.

Regards

guptadeva 2018-01-01 14:34

re-stating some of your quotes:

[QUOTE]I will post on this thread, once the thunder has passed,
the background work from which I derived the formula that I had posted

it involves an (elusive) prime relationship
time O(log n)
If authenticated, will compare to simplicity of Euclid's Proof for Infinite number of Primes[/QUOTE]

well, it was just a thunder in a water-glass so to say.
so i would still be interested to know more about
the method itself that led to your discovery

you managed to formulate a conclusion of your method in terms of
the mod function and this conclusion is equivalent to another conclusion of fermat

yet from your quotes i would deduce, that your original
method implies looking at some groups of the digits of
a number n ?

or do you just systematically play with numbers
on a computer and are able to spot interesting patterns
as the emerge ?

btw. fermat made quite a lot of hasty conclusions that were later proven to be wrong
(simple counter-examples), but this do not diminish his work ...
it just shows the necessity of formal proofs.

science_man_88 2018-01-01 14:40

[QUOTE=guptadeva;475839]re-stating some of your quotes:



well, it was just a thunder in a water-glass so to say.
so i would still be interested to know more about
the method itself that led to your discovery

you managed to formulate a conclusion of your method in terms of
the mod function and this conclusion is equivalent to another conclusion of fermat

yet from your quotes i would deduce, that your original
method implies looking at some groups of the digits of
a number n ?

or do you just systematically play with numbers
on a computer and are able to spot interesting patterns
as the emerge ?

btw. fermat made quite a lot of hasty conclusions that were later proven to be wrong
(simple counter-examples), but this do not diminish his work ...
it just shows the necessity of formal proofs.[/QUOTE]

Not to mention this is on of an infinite number of equivalents to Fermat's base 2 test.

guptadeva 2018-01-01 15:21

[QUOTE=science_man_88;475840]Not to mention this is on of an infinite number of equivalents to Fermat's base 2 test.[/QUOTE]
elementary my dear watson: all of these infinite number of tests are equivalent, yet some are more equivalent than others

xilman 2018-01-01 17:40

[QUOTE=gophne;475822]Hi chalsall

You point is taken.

I think you came from your mothers womb already filled with wisdom and magnanimity, because it is shining from you like a fiery beacon.

You are a colossus of a human being....there are and never will be anybody like you that will walk on this earth.

You must enjoy and never forget or let others forget this very special gift that you have been born with.

Go well.[/QUOTE]Flattery will get you everywhere.

science_man_88 2018-01-01 17:56

[QUOTE=guptadeva;475842]elementary my dear watson: all of these infinite number of tests are equivalent, yet some are more equivalent than others[/QUOTE]

And some could tell properties of n such that Mn have specific k in their divisors.

guptadeva 2018-01-01 18:30

[QUOTE=science_man_88;475857]And some could tell properties of n such that Mn have specific k in their divisors.[/QUOTE]

you are giving so many hints, dear sherlock :smile:

science_man_88 2018-01-01 19:31

[QUOTE=guptadeva;475863]you are giving so many hints, dear sherlock :smile:[/QUOTE]

Do they really count as hints if the person might not decipher them ?

guptadeva 2018-01-01 19:46

[QUOTE=science_man_88;475871]Do they really count as hints if the person might not decipher them ?[/QUOTE]

given enough hints, the person would't really need to decipher all of them in order to come to the right conclusion

Batalov 2018-01-01 20:54

Depends on a person!

Now, my question is this: wasn't this thread (and the poster) way better off when the thread was locked the first time?
Observe: the only thing that happened after reopening was that self-flagellation continued, followed by silent mediation. Sometimes I amazed how well I can see the (not so distant) future.

[QUOTE="Niels Bohr"]"[I]Prediction is very difficult[/I], [I]especially[/I] if it's about the [I]future[/I]."[/QUOTE]

ewmayer 2018-01-02 00:55

@Serge: I heard the "predictions are hard" quip attributed to Yogi Berra, not Bohr. Two names I never thought I'd see come up in the same sentence. :)

[url=https://quoteinvestigator.com/2013/10/20/no-predict/]Here is a detailed investigation[/url] into the history of said aphorism, which concludes that the saying is indeed most likely Danish in origin, but not due to Bohr. This sort of proliferation of attribution is quite common with especially pithy/witty sayings. To use a maths analogy, it's like people later slapping the name 'Gauss' on this, that or the other technique in order to boost its profile and/or legitimacy. (An example I recall from my days as a grad. student in fluid mechanics was something referred to as the "Gauss-Seidel" method, an iterative relaxation algorithm for solution of discretized elliptic PDEs. About which one of my profs commented, "Seidel didn't invent it and Gauss didn't work on it.")

chalsall 2018-01-02 01:08

[QUOTE=gophne;475822]I think you came from your mothers womb already filled with wisdom and magnanimity, because it is shining from you like a fiery beacon.[/QUOTE]

I came from my Mother's womb with a copy of "The Prince".

Which I then read.

guptadeva 2018-01-02 01:19

[URL]https://quoteinvestigator.com/2013/10/20/no-predict/[/URL]

does it really matter who said it first ? it's funny anyway
i.e. fermat is also "funny" :wink:

gophne 2018-01-02 01:48

[QUOTE=guptadeva;475839]re-stating some of your quotes:



well, it was just a thunder in a water-glass so to say.
so i would still be interested to know more about
the method itself that led to your discovery

you managed to formulate a conclusion of your method in terms of
the mod function and this conclusion is equivalent to another conclusion of fermat

yet from your quotes i would deduce, that your original
method implies looking at some groups of the digits of
a number n ?

or do you just systematically play with numbers
on a computer and are able to spot interesting patterns
as the emerge ?

btw. fermat made quite a lot of hasty conclusions that were later proven to be wrong
(simple counter-examples), but this do not diminish his work ...
it just shows the necessity of formal proofs.[/QUOTE]

Hi guptadeva

Thanx for your comments, and an opportunity, to provide the derivation of my now infamous algorithm.

I work with what I would call [I]number-grids[/I] a lot, whereby I take the postive integers, but mostly the odd numbers for obvious reasons, and arrange them into tables of varying number of columns, e.g.

01,03,05,07,09
11,13,15,17,19,
21,23,25,27,29,
31,33,35,37,39
41,43,45,47,49
51,53,55,57,59...this being a 5-column-grid of odd numbers.

Some interesting facts coming from this grid for example would be;

1) The columns filter the primes into primes having the same[I] unit digi[/I]t, i.e col-1 having all primes ending with the digit 1, column 2 has unit digit 3, and so on.
2) The grid filters out the mutiples of 5 for a grid with 5 columns, multiples of 7 for a grid with 7 columns, etc
3) The grids have the property that [I]per row[/I] (in a column), the values at that location, have the property of sieving out thevalue at that number of rows further down the column, e.g C1/R2 has a value of 11. All values in muliples of 11 would be composite. In C1/R2 the value is 21 and all numbers removed 21 rows from this location in the column, would be composite. Since 21 is a composite itself, with factors 3 & 7, all values removed both 3 and 7 rows from this location/value in the column would be composite as well. The rows/values not so eliminated are primes.

This makes these grids de facto, primality "sieves", which could actually be formulated/algorithmized as well.

When I tabulated the mersenne odd numbers vs modulo of the odd numbers (in Excel worksheets)....the quotions became bulky too quickly, I observed many interesting patterns for the results of the modulos...See extraction from the table/grid below;


01,02,03,04,05,06,07,08,09,10,11,12,13,14.......Column numbers
Row M -03,05,07,09,11,13,15,17,19,21,23,25,27,29.......Odd numbers
01 01 -01,01,01,01,01,01,01..........................................M mod Odd Number
02 03 -01,02,00,07,07,07,07,07,07,07,07,07,07,07,07
03 05 -01,01,03,04,09,05,01,14,12,10,08,06,04,02,00
04 07 -01,02,01,01,06,10,07,08,13,01,12,02,19,11,03
05 09 -01,01,00,07,05,04,01,01,17,07,05,11,25,18,15, etc.
06 11 -01,02,03,04,01,06,07,07,14,10,00,22,22,17,11

The M-column being the mersenne number 2^m-1, and the other columns being M [B]mod[/B] Odd number.

From this table many weird and wonderful properties were evident;

1) The M-column also has the sieve property [I]per row[/I] as discussed above (making it a de facto mersenne primality checker)
2) Within a column the modulos repeat itself according to definite pattern commensing with 1 and ending with the column number., albeit not always with a factor due to the primality of the mersenne primes. However, the table exposes a factor for M11 at Column 11, Odd number 23, the modulo returning 00
[I][B]3) The modulo of the row number equivalent vs the column number equivalent was always equal to the the row/column number itself, unless the odd number was composite![/B][/I]

Taking this relationship of the modulo for the mersenne number of a row [I]vs[/I] the odd number of the corresponding column, e.g. row 5, reduced to the following;

Row [B]5[/B] is equivalent to M9 and Col [B]5[/B] is equivalent to the odd number 11, WITH the modulo = "5"...which was apparently the case for all PRIME numbers (as tabulated per column).

The relationship was then, using the rule of "when the [I]modulo of row number equivalent vs column number equivalent = row/column number[/I] being prime", gave a relationship of M[I]n[/I] to Odd number (n+2), when the modulo was equal to the row/column number, being prime. For row 5, mersenne prime was "9", and the associated odd number "11", with the modulo for the function being "5", "5" being the mersenne index [(9) +1]/2.... I finally the reduced this to the formula/algorithm;

When [B]2^9-1 mod (9+2) == (9+1)/2, then (n+2)[/B] is prime according to the pattern that eminated from the table, Generalized, the formula became;

[B]When 2^n-1 mod (n+2) == (n+1)/2, (n+2) would be prime, else composite.[/B], according to the table I was working with which I took up to about +- 301

The table looked like a [I]rosetta stone[/I] for prime numbers (for the column odd numbers)

I then saw this relationship (in the table) as a relationship[I] that defines[/I] the relationship between prime numbers and composite numbers universally, with reference to the mersenne odd numbers.

That in a nutshell (forgive the pun) was how I derived the "algorithm" that I posted and was so enthusiastic about (without running it properly in SAGEMATH looking for things like false primes, etc, as I am still relatively inexperienced in Sagemath code).

An interesting thing about the table was also, in addition to the "grid-sieve" property of the mersenne numbers in Col-M (as nalluded to earlier), I also thought the table/algorithm could be used to identify "twin primes" tweaking the relationship/algorithm slightly to say that when two consecutive row/column equivalent modulos for the algorithm is equal to the row/column number, then we potentially have a twin prime! , barring false positives of course :(

That is it. That's how I came onto the relationship that I had posted.

chalsall 2018-01-02 01:50

[QUOTE=gophne;475909]That is it. That's how I came onto the relationship that I had posted.[/QUOTE]

Could you please elaborate?

gophne 2018-01-02 02:24

[QUOTE=chalsall;475910]Could you please elaborate?[/QUOTE]
Hi chalsall

I see you are a speed reader as well. Please speed read my post again.

chalsall 2018-01-02 02:27

[QUOTE=gophne;475912]I see you are a speed reader as well. Please speed read my post again.[/QUOTE]

Done. Next?

gophne 2018-01-02 02:29

[QUOTE=Batalov;475883]Depends on a person!

Now, my question is this: wasn't this thread (and the poster) way better off when the thread was locked the first time?
Observe: the only thing that happened after reopening was that self-flagellation continued, followed by silent mediation. Sometimes I amazed how well I can see the (not so distant) future.[/QUOTE]
Censorship has never worked...and will never work.

gophne 2018-01-02 02:32

[QUOTE=chalsall;475906]I came from my Mother's womb with a copy of "The Prince".

Which I then read.[/QUOTE]
Confirmation of your divinity.

chalsall 2018-01-02 02:32

[QUOTE=gophne;475914]Censorship has never worked...and will never work.[/QUOTE]

Oh. I thought you were going to ask me to pick a card. Any card.

chalsall 2018-01-02 02:33

[QUOTE=gophne;475915]Confirmation of your divinity.[/QUOTE]

A serious question: why are you here?

gophne 2018-01-02 02:35

[QUOTE=chalsall;475913]Done. Next?[/QUOTE]
Speed read it again.

gophne 2018-01-02 02:36

[QUOTE=chalsall;475917]A serious question: why are you here?[/QUOTE]
Reverse the question, why are you not doing your job in heaven?

guptadeva 2018-01-02 02:38

[QUOTE=gophne;475909]That is it. That's how I came onto the relationship that I had posted.[/QUOTE]

congratulations gophne, i understand - and good luck deciphereing more from "the rosetta-stone for primes" :smile:

p.s. there is also another set of rosetta stones for primes where the numbers inside change their positions of the numbers inside their grids. - one set of rosetta stones lead to the other ...

chalsall 2018-01-02 02:39

[QUOTE=gophne;475919]Reverse the question, why are you not doing your job in heaven?[/QUOTE]

That's really quite funny. But could also be interpreted as a threat on my life.

But seriously, what is the upside?

gophne 2018-01-02 02:44

[QUOTE=chalsall;475922]That's really quite funny. But could also be interpreted as a threat on my life.

But seriously, what is the upside?[/QUOTE]
Now you are being melodramatic chalsall! reminiscent of some of the caprious greek gods like Hades.

chalsall 2018-01-02 02:48

[QUOTE=gophne;475923]Now you are being melodramatic chalsall! reminiscent of some of the caprious greek gods like Hades.[/QUOTE]

As usual, you don't answer any questions.

Just radiate.

gophne 2018-01-02 02:50

[QUOTE=guptadeva;475921]congratulations gophne, i understand - and good luck deciphereing more from "the rosetta-stone for primes" :smile:

p.s. there are also other "rosetta stones for primes" with different numbering of the rows and columns[/QUOTE]
hi guptadeva

I not entirely sure whether this is a thumbs up or a thumbs down, but I want to be optimistic and think that it is a mild thumbs up.

Whatever the case, I have tried best that I can to respond to your request as I regard you comments to be very considered and neutral.

Thanx

guptadeva 2018-01-02 03:08

[QUOTE=gophne;475926]hi guptadeva

I not entirely sure whether this is a thumbs up or a thumbs down, but I want to be optimistic and think that it is a mild thumbs up.

Thanx[/QUOTE]

it is a big thumbs up
thank you for explaining your method.

p.s. the original p.s. has been altered slightly - and now it's time for me to leave this forum - going for a retreat.

gophne 2018-01-02 03:26

[QUOTE=guptadeva;475928]it is a big thumbs up
thank you for explaining your method.

p.s. the original p.s. has been altered slightly - and now it's time for me to leave this forum - going for a retreat.[/QUOTE]
Enjoy!

George M 2018-01-02 05:41

[QUOTE=gophne;475909]Hi guptadeva

Thanx for your comments, and an opportunity, to provide the derivation of my now infamous algorithm.

I work with what I would call [I]number-grids[/I] a lot, whereby I take the postive integers, but mostly the odd numbers for obvious reasons, and arrange them into tables of varying number of columns, e.g.

01,03,05,07,09
11,13,15,17,19,
21,23,25,27,29,
31,33,35,37,39
41,43,45,47,49
51,53,55,57,59...this being a 5-column-grid of odd numbers.

Some interesting facts coming from this grid for example would be;

1) The columns filter the primes into primes having the same[I] unit digi[/I]t, i.e col-1 having all primes ending with the digit 1, column 2 has unit digit 3, and so on.
2) The grid filters out the mutiples of 5 for a grid with 5 columns, multiples of 7 for a grid with 7 columns, etc
3) The grids have the property that [I]per row[/I] (in a column), the values at that location, have the property of sieving out thevalue at that number of rows further down the column, e.g C1/R2 has a value of 11. All values in muliples of 11 would be composite. In C1/R2 the value is 21 and all numbers removed 21 rows from this location in the column, would be composite. Since 21 is a composite itself, with factors 3 & 7, all values removed both 3 and 7 rows from this location/value in the column would be composite as well. The rows/values not so eliminated are primes.

This makes these grids de facto, primality "sieves", which could actually be formulated/algorithmized as well.

When I tabulated the mersenne odd numbers vs modulo of the odd numbers (in Excel worksheets)....the quotions became bulky too quickly, I observed many interesting patterns for the results of the modulos...See extraction from the table/grid below;


01,02,03,04,05,06,07,08,09,10,11,12,13,14.......Column numbers
Row M -03,05,07,09,11,13,15,17,19,21,23,25,27,29.......Odd numbers
01 01 -01,01,01,01,01,01,01..........................................M mod Odd Number
02 03 -01,02,00,07,07,07,07,07,07,07,07,07,07,07,07
03 05 -01,01,03,04,09,05,01,14,12,10,08,06,04,02,00
04 07 -01,02,01,01,06,10,07,08,13,01,12,02,19,11,03
05 09 -01,01,00,07,05,04,01,01,17,07,05,11,25,18,15, etc.
06 11 -01,02,03,04,01,06,07,07,14,10,00,22,22,17,11

The M-column being the mersenne number 2^m-1, and the other columns being M [B]mod[/B] Odd number.

From this table many weird and wonderful properties were evident;

1) The M-column also has the sieve property [I]per row[/I] as discussed above (making it a de facto mersenne primality checker)
2) Within a column the modulos repeat itself according to definite pattern commensing with 1 and ending with the column number., albeit not always with a factor due to the primality of the mersenne primes. However, the table exposes a factor for M11 at Column 11, Odd number 23, the modulo returning 00
[I][B]3) The modulo of the row number equivalent vs the column number equivalent was always equal to the the row/column number itself, unless the odd number was composite![/B][/I]

Taking this relationship of the modulo for the mersenne number of a row [I]vs[/I] the odd number of the corresponding column, e.g. row 5, reduced to the following;

Row [B]5[/B] is equivalent to M9 and Col [B]5[/B] is equivalent to the odd number 11, WITH the modulo = "5"...which was apparently the case for all PRIME numbers (as tabulated per column).

The relationship was then, using the rule of "when the [I]modulo of row number equivalent vs column number equivalent = row/column number[/I] being prime", gave a relationship of M[I]n[/I] to Odd number (n+2), when the modulo was equal to the row/column number, being prime. For row 5, mersenne prime was "9", and the associated odd number "11", with the modulo for the function being "5", "5" being the mersenne index [(9) +1]/2.... I finally the reduced this to the formula/algorithm;

When [B]2^9-1 mod (9+2) == (9+1)/2, then (n+2)[/B] is prime according to the pattern that eminated from the table, Generalized, the formula became;

[B]When 2^n-1 mod (n+2) == (n+1)/2, (n+2) would be prime, else composite.[/B], according to the table I was working with which I took up to about +- 301

The table looked like a [I]rosetta stone[/I] for prime numbers (for the column odd numbers)

I then saw this relationship (in the table) as a relationship[I] that defines[/I] the relationship between prime numbers and composite numbers universally, with reference to the mersenne odd numbers.

That in a nutshell (forgive the pun) was how I derived the "algorithm" that I posted and was so enthusiastic about (without running it properly in SAGEMATH looking for things like false primes, etc, as I am still relatively inexperienced in Sagemath code).

An interesting thing about the table was also, in addition to the "grid-sieve" property of the mersenne numbers in Col-M (as nalluded to earlier), I also thought the table/algorithm could be used to identify "twin primes" tweaking the relationship/algorithm slightly to say that when two consecutive row/column equivalent modulos for the algorithm is equal to the row/column number, then we potentially have a twin prime! , barring false positives of course :(

That is it. That's how I came onto the relationship that I had posted.[/QUOTE]

To those who ever thought gophne was a liar (and to those who are just curious, like me). By the way, gophne, certain types of grids are known as arrays and/or matrices.

CRGreathouse 2018-01-02 06:47

[QUOTE=gophne;475909]I work with what I would call [I]number-grids[/I] a lot, whereby I take the postive integers, but mostly the odd numbers for obvious reasons, and arrange them into tables of varying number of columns, e.g.

01,03,05,07,09
11,13,15,17,19,
21,23,25,27,29,
31,33,35,37,39
41,43,45,47,49
51,53,55,57,59...this being a 5-column-grid of odd numbers.

Some interesting facts coming from this grid for example would be;

1) The columns filter the primes into primes having the same[I] unit digi[/I]t, i.e col-1 having all primes ending with the digit 1, column 2 has unit digit 3, and so on.
2) The grid filters out the mutiples of 5 for a grid with 5 columns, multiples of 7 for a grid with 7 columns, etc
3) The grids have the property that [I]per row[/I] (in a column), the values at that location, have the property of sieving out thevalue at that number of rows further down the column, e.g C1/R2 has a value of 11. All values in muliples of 11 would be composite. In C1/R2 the value is 21 and all numbers removed 21 rows from this location in the column, would be composite. Since 21 is a composite itself, with factors 3 & 7, all values removed both 3 and 7 rows from this location/value in the column would be composite as well. The rows/values not so eliminated are primes.

This makes these grids de facto, primality "sieves", which could actually be formulated/algorithmized as well.[/QUOTE]

These are usually called "wheels", as in [url=https://en.wikipedia.org/wiki/Wheel_factorization]wheel factorization[/url].

gophne 2018-01-02 07:36

[QUOTE=CRGreathouse;475959]These are usually called "wheels", as in [url=https://en.wikipedia.org/wiki/Wheel_factorization]wheel factorization[/url].[/QUOTE]
Hi CRGreathouse

Thanks. I will read up more about this.

My references/material are sourced mostly from Wikipedia and youtube.

I will follow you link as well.

Regards

gophne 2018-01-02 16:54

[QUOTE=CRGreathouse;475959]These are usually called "wheels", as in [url=https://en.wikipedia.org/wiki/Wheel_factorization]wheel factorization[/url].[/QUOTE]
Hi CRGreathouse

I read up on your link about [I]wheel factorization[/I], and it is unfortunately a bit too complicated for me to understand the math involved in [I]wheel factorization[/I] fully at this stage. It seems as if one would need to have a post-grad qualification in [I]wheel factorization[/I] to fully understand it.

What I do is much simpler. I take the positive odd numbers and arrange them into grids of varying column numbers, and then look at the distribution patterns of the prime numbers. For example again, if I arrange the odd numbers into a 3-column grid (or an [I]array[/I] as one of the other contributors has suggested that it could be called), all the primes are then distrubuted in columns 1 & 3 respectively, and column 2 contains "3" and all the odd multiples of three. Column 3 contains all the [I]chen primes[/I], as well as all the squares of the odd numbers(including primes) in column 1. Column 1 contains all the primes that would follow after chen primes -that is the second partner of [I]twin primes[/I], as well as the squares of the odd numbers (including primes) in column 3). Just some of the more obvious patterns eminating fro a 3-column grid.

As indicated in an earlier post, these tables have the property of being de facto primality sieves as well. The prime (and composites) in this [I]grid-3[/I] distribution are distributed according to 6n+1, 6n-1 consecutive order. Again the sieve factor can be algorithmized to identify the prime distribution in this grid.

Grids with a prime number of columns, "filters" the multiples of that prime number located in the centre column of the grid. Grids with a composite number of columns "filters" all the prime factors of that composite odd number!! Another potential algorithm! which would read something as follows;

[B]For any XXX-grid of odd prime numbers with y number of columns, where [I]y[/I] is an element of the set of odd numbers, then when [I]y[/I] is prime, only one set of odd multiples of [I]y[/I] would be distributed in the centre column of the the grid.
If y is composite, the multiples of the [I]prime factors[/I] of [I]y[/I] will be "filtered" on both sides of the grid, with respect to the [I]y[/I](composite)-multiples in the centre column. [/B]

[I]Caveat: Not sure if anybody else has done or publish similar work (Odd No.Grid-Column no. relationships), but the above is only for information with respect to what I have worked with.[/I]

ET_ 2018-01-02 17:18

[QUOTE=gophne;476046]Hi CRGreathouse

I read up on your link about [I]wheel factorization[/I], and it is unfortunately a bit too complicated for me to understand the math involved in [I]wheel factorization[/I] fully at this stage. It seems as if one would need to have a post-grad qualification in [I]wheel factorization[/I] to fully understand it.
[/QUOTE]

What CRGreathouse published does not need a post-grad qualification: it only needs 10th grade math, patience, will and attention. It looks like you don't have any of such qualities, if you did not get to the end of the document he linked.

Patience, will and attention: if you lack such elementary attitudes, you will never, never succeed in math.

M344587487 2018-01-02 17:20

[QUOTE=gophne;476046]...
I read up on your link about [I]wheel factorization[/I], and it is unfortunately a bit too complicated for me to understand the math involved in [I]wheel factorization[/I] fully at this stage. It seems as if one would need to have a post-grad qualification in [I]wheel factorization[/I] to fully understand it.
...[/QUOTE]

Can you not follow the algorithm, or is it trying to understand how the algorithm works that is too complicated?

Batalov 2018-01-02 18:31

1 Attachment(s)
[QUOTE=gophne;476046]
[I]Caveat: Not sure if anybody else has done or publish similar work, but the above is only for information with respect to what I have worked with.[/I][/QUOTE]
This is solipsism. This can be justified in the case of complete deaf-blindness, but in other cases usually stems from extreme ignorance. You are definitely not 5 years old - you use big words like "post-grad qualification". Why do you act like a 5 year-old? You shout. You behave cranky. You mess around in all the rooms of this virtual space... We are all baffled.

Think about it.

gophne 2018-01-03 00:26

Moving into Stormy Waters
 
My mom always used to teach me....Son, when you hear wolves howling in unison, protect the chicken-pen!

chalsall 2018-01-03 01:04

[QUOTE=gophne;476084]My mom always used to teach me....[/QUOTE]

Did she teach you, or tell you? Very different things.

danaj 2018-01-03 01:21

I'm sure there are plenty of other examples, some better, but a paper I ran across when I was first serously fiddling with these things, shows a number of similar charts (see page 106-107 near the end). Arranging numbers in an array and noticing patterns of primes and composites is common.

"[URL="http://www.mat.ucm.es/serv/revmat/vol9-1/vol9-1e.pdf"]A Note on the Extensions of Eratosthenes' Sieve[/URL]" by Quesada and Van Pelt, [B][COLOR="Red"]1996[/COLOR][/B]. By today's standards this is pretty yawn-worthy, but I personally gained some appreciation of the modular patterns from reading it, as well as some ideas for optimizing my SoE implementation back when I first started it (so many things I didn't know then....) I don't think the authors believed they were making really novel insights, but trying to make some helpful clarifications and noting patterns.

Feel free to make these connections, not read anything of the previous work in the field, and believe you are a genius first discoverer. That's great. I am somewhat envious. But I'd also know I was lying to myself.

[quote]Son, when you hear wolves howling in unison, protect the chicken-pen![/quote]

"They laughed at Einstein, but they also laughed at Bozo the clown."

This is crank-thought (there should be some cool German word for this). The more people disagree with you, the more you must be a misunderstood genius?

chalsall 2018-01-03 01:37

[QUOTE=danaj;476090]The more people disagree with you, the more you must be a misunderstood genius?[/QUOTE]

It's all cool dude. Everyone here knows that gophne isn't serious. He's just pushing buttons.

LaurV 2018-01-03 06:05

[QUOTE=gophne;475516]x==y mod x.
[/QUOTE]
0==0.
Always.
:razz:

George M 2018-01-03 06:18

[QUOTE=chalsall;476091]It's all cool dude. Everyone here knows that gophne isn't serious. He's just pushing buttons.[/QUOTE]

I don’t think it is right to say, “Everyone knows...”. At the end of the day, this is a mere assumption on your behalf, but most likely everyone else’s; it is just a perceived truth, and thus shouldn’t be stated with such certainty.

MisterBitcoin 2018-01-03 06:20

[QUOTE=danaj;476090]
This is crank-thought (there should be some cool German word for this).[/QUOTE]



Thats hard. It means "Kurbel Gedanke", well thats not even a real word anyway. :smile:
Well the translator is blocked from my office, but I guess you mean something like "besondere Gedanken" or especially thoughts.

MisterBitcoin 2018-01-03 06:24

[QUOTE=George M;476114]I don’t think it is right to say, “Everyone knows...”. At the end of the day, this is a mere assumption on your behalf, but most likely everyone else’s; it is just a perceived truth, and thus shouldn’t be stated with such certainty.[/QUOTE]



He can´t be serios, just saying. Nearly anyone who read this thread knows it.

George M 2018-01-03 06:26

[QUOTE=MisterBitcoin;476116]He can´t be serios, just saying. Nearly anyone who read this thread knows it.[/QUOTE]

Look, I understand where you’re coming from, but I’m just trying to prevent any further action of this sort to be taken so that no people feel harmed and unsafe.

LaurV 2018-01-03 06:41

[QUOTE=chalsall;475808]If I may please say, you are quite possibly the funniest AI we've ever had here.
[/QUOTE]
I also wondered that, for the last 15 minutes I wasted of my life, reading this thread. The pattern is bot-typical, but I don't think he is a bot, he is just a trlol. He knows some math terms and knows how to use them in context, which is quite difficult for a bot. It is not just Eliza, like storfly and other "guys" we had here around. This guy is more in the "cmd" category.

We may think to a method to catch him/her/it in the future, but for now, the best, unless you think the fun is worth, would be:
:dnftt:
and we consider it was good what Serge did, to lcok the therad.

danaj 2018-01-03 08:00

[QUOTE=MisterBitcoin;476115]Thats hard. It means "Kurbel Gedanke", well thats not even a real word anyway. :smile:
Well the translator is blocked from my office, but I guess you mean something like "besondere Gedanken" or especially thoughts.[/QUOTE]

The best I could come up with was exzentrisches Denken or maybe verdrehter Gedanken, but my German is quite poor. I was hoping for some nice compound word, like Fremdschämen or Treppenwitz. Ich habe Weltschmerz weil es kein Wort gibt.

gophne 2018-01-05 15:41

[QUOTE=danaj;476090]I'm sure there are plenty of other examples, some better, but a paper I ran across when I was first serously fiddling with these things, shows a number of similar charts (see page 106-107 near the end). Arranging numbers in an array and noticing patterns of primes and composites is common.

"[URL="http://www.mat.ucm.es/serv/revmat/vol9-1/vol9-1e.pdf"]A Note on the Extensions of Eratosthenes' Sieve[/URL]" by Quesada and Van Pelt, [B][COLOR="Red"]1996[/COLOR][/B]. By today's standards this is pretty yawn-worthy, but I personally gained some appreciation of the modular patterns from reading it, as well as some ideas for optimizing my SoE implementation back when I first started it (so many things I didn't know then....) I don't think the authors believed they were making really novel insights, but trying to make some helpful clarifications and noting patterns.

Feel free to make these connections, not read anything of the previous work in the field, and believe you are a genius first discoverer. That's great. I am somewhat envious. But I'd also know I was lying to myself.



"They laughed at Einstein, but they also laughed at Bozo the clown."

This is crank-thought (there should be some cool German word for this). The more people disagree with you, the more you must be a misunderstood genius?[/QUOTE]

Hi Guys, Apologies I had some other business to attend to so I could unfortunately not reply earlier.

Danaj, did you read the link/paper that you posted. If you have, which i doubt, I think you simply "googled" a paper which you thought might support your argument.

Honestly, if you really think that is EASY math, equivalent to what I have introduced to you, then you need to change your medication.

I leave it to all the hundreds of neutral readers out there to decide. I shall be happy with that.

I am in the process of preparing to submit my algorithms to other sites/forums, as well, SO THAT ANY FRAUDULENCY COULD BE EXPOSED FAR AND WIDE, but not by an apparent biased grouping.

Look I might be proved to be the world's greatest fraud in the end, but I believe in my own integrity.
That there might be work out there that predates/expounds on what I claim/submit is not at issue, being cogniscent of the wealth of brain power that is involved in the field of math all over the world.

But what I do know that soon very soon at least one reader/contributor would appraciate what I have "discovered", much of which I have not posted, fearing a witch-hunt of the order of the Inquisition of the Dark Ages. The more times change....the more they remain the same.

On this site, I don't expect a symphatetic ear to anything I say, sad but true. I don't know if there are any other contributers that get that feeling as well, or if i am imagining myself.

However, very soon (about a month or two) if I would be able to still post, I would like to attempt a Proof for the Twin Prime Conjecture. Not sure if it would be a valid proof. But I can already see the commentary in my minds eye if the proof should be successful;

"What a fraud and cheat!!!! That proof has already been done by the Easter Bunny during the Munich October Bierfest, using invisible ink! Off with his head!"

Winston Churchill was supposed to have said,
"If you are going through hell, keep going." ......Source [url]www.goodreads.com[/url]

jnml 2018-01-05 15:54

1 Attachment(s)
[QUOTE=gophne;476516]
However, very soon (about a month or two) if I would be able to still post, I would like to attempt a Proof for the Twin Prime Conjecture. Not sure if it would be a valid proof. But I can already see the commentary in my minds eye if the proof should be successful;
[/QUOTE]

Sure.

gophne 2018-01-05 15:55

[QUOTE=LaurV;476122]I also wondered that, for the last 15 minutes I wasted of my life, reading this thread. The pattern is bot-typical, but I don't think he is a bot, he is just a trlol. He knows some math terms and knows how to use them in context, which is quite difficult for a bot. It is not just Eliza, like storfly and other "guys" we had here around. This guy is more in the "cmd" category.

We may think to a method to catch him/her/it in the future, but for now, the best, unless you think the fun is worth, would be:
:dnftt:
and we consider it was good what Serge did, to lcok the therad.[/QUOTE]
LuarV

You cannot be serious as well , can you? Are you openly propagating censorship and oppression of ideas (scientific or otherwise) in this day and age?

Are you even from this planet?

If you are serious, then I have no words for you, and won't be commenting on any of your posts in future. But you can continue to post whatever you like on this forum, no problem, since it would add to the debate.

science_man_88 2018-01-05 16:29

[QUOTE=gophne;476516]Hi Guys, Apologies I had some other business to attend to so I could unfortunately not reply earlier.

Danaj, did you read the link/paper that you posted. If you have, which i doubt, I think you simply "googled" a paper which you thought might support your argument.

Honestly, if you really think that is EASY math, equivalent to what I have introduced to you, then you need to change your medication.

I leave it to all the hundreds of neutral readers out there to decide. I shall be happy with that.

I am in the process of preparing to submit my algorithms to other sites/forums, as well, SO THAT ANY FRAUDULENCY COULD BE EXPOSED FAR AND WIDE, but not by an apparent biased grouping.

Look I might be proved to be the world's greatest fraud in the end, but I believe in my own integrity.
That there might be work out there that predates/expounds on what I claim/submit is not at issue, being cogniscent of the wealth of brain power that is involved in the field of math all over the world.

But what I do know that soon very soon at least one reader/contributor would appraciate what I have "discovered", much of which I have not posted, fearing a witch-hunt of the order of the Inquisition of the Dark Ages. The more times change....the more they remain the same.

On this site, I don't expect a symphatetic ear to anything I say, sad but true. I don't know if there are any other contributers that get that feeling as well, or if i am imagining myself.

However, very soon (about a month or two) if I would be able to still post, I would like to attempt a Proof for the Twin Prime Conjecture. Not sure if it would be a valid proof. But I can already see the commentary in my minds eye if the proof should be successful;

"What a fraud and cheat!!!! That proof has already been done by the Easter Bunny during the Munich October Bierfest, using invisible ink! Off with his head!"

Winston Churchill was supposed to have said,
"If you are going through hell, keep going." ......Source [url]www.goodreads.com[/url][/QUOTE]
I think you would've got a better reception had you asked is this a new result off the bat. Math comes down to proofs axioms and definitions. That determines the outcome.

Nick 2018-01-05 17:32

@gophne:
You appear to be experiencing [URL="https://en.wikipedia.org/wiki/Culture_shock"]culture shock[/URL].

Imagine spending some time at one of the world's top universities.
You would find spaces devoted to socializing, spaces for education, and other spaces dedicated to research.
In the research spaces, the focus would be on ideas and results, at a very high level, and not on people.
Everyone is extremely critical of new ideas because that way we make progress faster.

This forum is organized in much the same way.
To socialize, you can browse people's posts and react in the Lounge or the Soap Box.
To learn the basics, head for the Number Theory Discussion Group.
But in the parts of the forum dedicated to new ideas and results, you can expect us to be highly critical and focus on the concepts, not the people.
You say you arrived at your results independently and worked very hard to do so. We do not doubt it.
But once it became clear that your result was equivalent to something already well known, we lost interest.
That is not personal - our reaction would have been the same whoever presented the idea. It is the normal culture in research.

CRGreathouse 2018-01-05 17:55

[QUOTE=gophne;476516]Danaj, did you read the link/paper that you posted. If you have, which i doubt, I think you simply "googled" a paper which you thought might support your argument.[/QUOTE]

Danaj is an expert, the author of [url=http://search.cpan.org/~danaj/Math-Prime-Util-0.69/lib/Math/Prime/Util.pm]Math::Prime::Util[/url] among others. He certainly did not just Google up a random paper.

[QUOTE=gophne;476516]Honestly, if you really think that is EASY math, equivalent to what I have introduced to you, then you need to change your medication.[/QUOTE]

Wheel sieves and splitting consecutive integers into columns representing congruence classes mod the width are very easy math, yes. The Quesada & Van Pelt paper contains more advanced mathematics as well (but nothing terribly difficult, on a glance).

[QUOTE=gophne;476516]I am in the process of preparing to submit my algorithms to other sites/forums, as well, SO THAT ANY FRAUDULENCY COULD BE EXPOSED FAR AND WIDE, but not by an apparent biased grouping.[/QUOTE]

That sounds like a plan. With any luck you'll get useful feedback elsewhere that will improve your exposition etc.

[QUOTE=gophne;476516]Look I might be proved to be the world's greatest fraud in the end, but I believe in my own integrity.[/QUOTE]

Rediscovery is very common in mathematics, it's nothing to be ashamed of. (I don't think anyone here is impugning your integrity.) Ramanujan rediscovered a tremendous number of results and no one thought any less of him as a result. But if you want to publish you have a scholarly obligation to search for prior art and attribute original ideas to their respective discoverers. (There are plenty of papers out there reproving known theorems, just because the proofs are easier, shorter, or more enlightening -- but they are expected to cite the original work, even if their discovery was independent.)

[QUOTE=gophne;476516]But what I do know that soon very soon at least one reader/contributor would appraciate what I have "discovered", much of which I have not posted, fearing a witch-hunt of the order of the Inquisition of the Dark Ages. The more times change....the more they remain the same.[/QUOTE]

That's a bit melodramatic, don't you think? Thousands were tortured or executed in the Inquisition, whereas here not only is no one hurting or silencing you, but you're even being provided a platform, for free, on which to express your thoughts.

[QUOTE=gophne;476516]However, very soon (about a month or two) if I would be able to still post, I would like to attempt a Proof for the Twin Prime Conjecture.[/QUOTE]

I'm not surprised -- there have been dozens if not hundreds of claimed proofs of the twin prime conjecture, it's one of the most popular targets of cranks. Dudley has two or three books on the general subject, though I don't recall if he included examples of twin primes proofs.

[QUOTE=gophne;476516]Not sure if it would be a valid proof.[/QUOTE]

That modesty might be your saving grace. Good luck, and may your proofs always hold. :smile:

CRGreathouse 2018-01-05 17:58

[QUOTE=Nick;476531]Imagine spending some time at one of the world's top universities.
You would find spaces devoted to socializing, spaces for education, and other spaces dedicated to research.
In the research spaces, the focus would be on ideas and results, at a very high level, and not on people.
Everyone is extremely critical of new ideas because that way we make progress faster.

This forum is organized in much the same way.
To socialize, you can browse people's posts and react in the Lounge or the Soap Box.
To learn the basics, head for the Number Theory Discussion Group.
But in the parts of the forum dedicated to new ideas and results, you can expect us to be highly critical and focus on the concepts, not the people.
You say you arrived at your results independently and worked very hard to do so. We do not doubt it.
But once it became clear that your result was equivalent to something already well known, we lost interest.
That is not personal - our reaction would have been the same whoever presented the idea. It is the normal culture in research.[/QUOTE]

Well said.

gophne 2018-01-05 18:28

[QUOTE=Nick;476531]@gophne:
You appear to be experiencing [URL="https://en.wikipedia.org/wiki/Culture_shock"]culture shock[/URL].

Imagine spending some time at one of the world's top universities.
You would find spaces devoted to socializing, spaces for education, and other spaces dedicated to research.
In the research spaces, the focus would be on ideas and results, at a very high level, and not on people.
Everyone is extremely critical of new ideas because that way we make progress faster.

This forum is organized in much the same way.
To socialize, you can browse people's posts and react in the Lounge or the Soap Box.
To learn the basics, head for the Number Theory Discussion Group.
But in the parts of the forum dedicated to new ideas and results, you can expect us to be highly critical and focus on the concepts, not the people.
You say you arrived at your results independently and worked very hard to do so. We do not doubt it.
But once it became clear that your result was equivalent to something already well known, we lost interest.
That is not personal - our reaction would have been the same whoever presented the idea. It is the normal culture in research.[/QUOTE]
Hi Nick

Good post, I like it very much (I do not know yet how to add smileys to post like some of the other contributors, but I would have liked to add a "good post" smiley to your post, because eventhough you are very thorough and firm in your stance (and clearly not impressed with time wasting and spiels), you never-the-less criticise in such a way that it actually feels good! Seriously.

For your information I am contesting the verdict that the algorithm in question was in fact a copy or clone (of Fermat's Primality Test or another)...BUT NOT ON THIS SITE OT THREAD, I promise!!!!!!

I am contesting this finding on five grounds (I am working with friends who are having another closer look at this matter and the supporting premises for the current accepted status, much of it which is due to my own acceptance of the suggestions of sameness), but the conundrum is this as well....I am such a dunce, why is it that when I accept suggestions of the "sameness" of the posted algorith, I suddenly become a guruji.

For you information, should you be interested at all, which I doubt and don't blame you for, and won't bore you with it as well! the grounds for the contestation are the follow, just for the information of other readers;

1) Fermat's Primality test works with congruancy, whilst the accused algorithm works with equality (changing remainders for changing inputs)

2) Reducing the formula's of the two algorithms to standard form, [B]LHS mod x[/B], furnishes different dividends.

3) Changing the base of the dividend from base 2, does not furnish the same remainders. For Fermat's Primality the remainder/congruancy is always one(1) for prime witness.

4) Fermat's Primality Test does not utilize [I]mersenne numbers[/I] at all! the accused algorithm has the mersenne form as the dividend of the algorithm!

5) Running the suspect algorithm for false negatives up to 1,000,000 none was found -This has been confirmed unintentionally by one of the senior contributors on the site that was running the algorithm in Pari, I think -check some of the earlier posts.
Fermat's Primality check has a problem with false negatives (Carmichael Numbers).

It is only over once the fat lady sings, but this is not for this Site or Forum.

Thanx and regards.

jnml 2018-01-05 18:35

[QUOTE=gophne;476550]
5) Running the suspect algorithm for false negatives up to 1,000,000 none was found -This has been confirmed unintentionally by one of the senior contributors on the site that was running the algorithm in Pari, I think -check some of the earlier posts.
Fermat's Primality check has a problem with false negatives (Carmichael Numbers).
[/QUOTE]

Please link that post you're talking about, I'm not sure which you mean, thanks.

gophne 2018-01-05 18:38

[QUOTE=jnml;476519]Sure.[/QUOTE]
Hi jnml

Don't be so harsh on yourself. I know the feeling too.

gophne 2018-01-05 18:54

[QUOTE=CRGreathouse;476538]Danaj is an expert, the author of [url=http://search.cpan.org/~danaj/Math-Prime-Util-0.69/lib/Math/Prime/Util.pm]Math::Prime::Util[/url] among others. He certainly did not just Google up a random paper.



Wheel sieves and splitting consecutive integers into columns representing congruence classes mod the width are very easy math, yes. The Quesada & Van Pelt paper contains more advanced mathematics as well (but nothing terribly difficult, on a glance).



That sounds like a plan. With any luck you'll get useful feedback elsewhere that will improve your exposition etc.



Rediscovery is very common in mathematics, it's nothing to be ashamed of. (I don't think anyone here is impugning your integrity.) Ramanujan rediscovered a tremendous number of results and no one thought any less of him as a result. But if you want to publish you have a scholarly obligation to search for prior art and attribute original ideas to their respective discoverers. (There are plenty of papers out there reproving known theorems, just because the proofs are easier, shorter, or more enlightening -- but they are expected to cite the original work, even if their discovery was independent.)



That's a bit melodramatic, don't you think? Thousands were tortured or executed in the Inquisition, whereas here not only is no one hurting or silencing you, but you're even being provided a platform, for free, on which to express your thoughts.



I'm not surprised -- there have been dozens if not hundreds of claimed proofs of the twin prime conjecture, it's one of the most popular targets of cranks. Dudley has two or three books on the general subject, though I don't recall if he included examples of twin primes proofs.



That modesty might be your saving grace. Good luck, and may your proofs always hold. :smile:[/QUOTE]
Hi CRGreathouse

I like everything you say, and finds your comments very uplifting, yet firm yet balanced.

I shall take to heart all you say and model my responses making use of your counsel.

What can I say, ever since my first post on this thread, making [I]outlandish[/I] claims, you have been very positive yet authoritive in demanding a professional standard w.r.t claims made, research done, supporting evidence required, etc. You came/come accross as a Sage who can see the folly in other mortals, but do not stamp on them like they are insects because of their ignorance/stubbornness/foolhardiness. For this I thank you, and I think I speak for many others, especially the inexperienced contributors on the site.

Whatever happens on the site/thread in days to come, I will only have gratitude for your approach, even to the unwise, as I admit I could be, or possibly am.


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