Are Legendre symbols proven to be defective?

[PaulJobling]

Originally Posted by jasong

I fully expect to discover that 769 DOESN'T divide the number. I believe the only numbers that divide 2^3355584+1 are 1 and 2^3355584+1.

2^3355584+1=(2^1118528+1) x (2^2237056-2^1118528+1)

[ET_]

Originally Posted by Richard Cameron

Happy Birthday.

I note that you are a Piscean whilst I, born just a few days later am an Aries. Correspondingly, our natures will be very different.

Richard.

Happy birthday David. I got 46 on 7th...

Luigi

[Mini-Geek]

Originally Posted by PaulJobling

2^3355584+1=(2^1118528+1) x (2^2237056-2^1118528+1)

I just made Pari/GP output those two things to files and compared them with COMP. Guess what, they're precisely the same...big surprise.

Jasong, you know of a way you can prove or disprove that 769 divides 2^3355584+1? Write it out on paper using a calculator to assist you (unless they're in the conspiracy, too).
Be my guest. Multiply 2 by itself 3,355,584 times then add one (or have the computer do this part if you trust it for that) and manually divide that by 769.
Just don't make a single mistake during any of it, and you'll be fine.

If all the major chip makers are reducing their precision, how do you plan to prove that 2^3355584+1 is prime? With an iPod? Graphing calculator maybe? Have fun waiting years for it to finish...

[rogue]

Originally Posted by jasong

It will never show up on the Prime Pages because LLR is flawed, not because of theory or programming, but because Intel chips are flawed. It would also appear that AMD is attempting similar tactics to attempt to get their performance crown back, so applications that require a very high amount of precision are going to be very screwed in the future, though DC projects of that sort already are.

The presumption that LLR (or PRP, Prime95, PFGW) being incorrect just because they run on Intel chips is flawed. What jasong forgets is that LLR can run on any CPU in the x86 family, chips made by both Intel and AMD, from the 386 to the P4 to the Sempron to the Core 2 Duo. Is he saying that all versions of x86 are flawed and have the same flaw? He also forgets that most numbers on the Prime Pages can be verified on non-x86 hardware (although it takes more time). Is he saying that all chips, even non-x86 chips, have a flaw introduced by Intel?

Originally Posted by jasong

For those of you who require proof, I have lost all respect for this forum, so don't really care what people believe. This post is what is called closure.

As far as I am concerned, go and go quickly. I don't think many of us will miss you. You had many opportunities to learn from this forum, some in this thread. We cannot help you if you choose to refuse those opportunities. Maybe you should join Ttn and his project...

As a warning to everyone else, I expect his vitriol to carry over to the other forums that he participates in. I've had similar run-ins with him elsewhere for the same reasons that we see in this thread, specifically, he refuses to accept that some people know far more than he does about sieving, factoring, and PRP testing. Although I tend to be a little more civil than Bob, I also tend to be a little more sarcastic and like to point out flaws in logic, which has put me on jasong's and Ttn's *hit lit. Their problem is that they tend to refuse to admit that they are wrong.

Originally Posted by jasong

Goodbye, and may your fish dinners contain bones, and may your bowel movements be bloody, hard, and painful.

To jasong: So Long, and Thanks for All the Fish

[Orgasmic Troll]

Originally Posted by jasong

The idea that would have any respect for your opinion at all at this point is laughable. I view you the same way you view Hitler, and that is not an understatement. You have a murderous heart and you will probably be close enough to hear his screams when you reach your true home.

The idea that this Forum is referred to as a math forum is a sick joke. The forums at this site that are either fun or productive are fun because math isn't discussed in them, and when it is, the normal suspects generally aren't aware of it, so things tend to stay civil. The various prime projects are fun because the smart-asses that are so smug about the knowledge don't tend to discuss it in those forums, probably because they aren't there to have a good time, but to degrade people. The factoring forum is tolerable, or not, depending on what the subject matter is. If people come here to learn math, of just about any sort, there is a better than even chance that they will be insulted within a few hours of starting their thread.

For those of you who come here to discover prime numbers, I hope you enjoy your stay. I would encourage you to take specifically mathematical questions to other forums, or use Google.

As far as the unanswered questions are concerned, I say to R.D. Silverman and the other people who have insulted me(with the exception of wblipp. If he distances himself from me on this, I am not hurt. Whatever his opinion of me, I would love to crunch his project in the future, since he generally seems to be a fairly kind individual.) FUCK YOU!!! If you wish to know how my trials go with testing (2^3355584+1)/769, you may inquire at Riesel Sieve Forum in a week or two. I fully expect to discover that 769 DOESN'T divide the number. I believe the only numbers that divide 2^3355584+1 are 1 and 2^3355584+1. It will never show up on the Prime Pages because LLR is flawed, not because of theory or programming, but because Intel chips are flawed. It would also appear that AMD is attempting similar tactics to attempt to get their performance crown back, so applications that require a very high amount of precision are going to be very screwed in the future, though DC projects of that sort already are. For those of you who require proof, I have lost all respect for this forum, so don't really care what people believe. This post is what is called closure.

Goodbye, and may your fish dinners contain bones, and may your bowel movements be bloody, hard, and painful.

Mathematics is not for the weak-hearted or the easily upset. Silverman has a point, whether or not you agree with his delivery.

You come in here spouting nonsense. You aren't even aware that it's nonsense. You refuse to learn. You refuse to go read the books that people tell you to read. You get some wild-ass idea (which is fine!) and then ask for information about it, and then when someone tells you where to find more information, you abandon the idea (which is not fine!). You wanted to tell us "FUCK YOU"? Every time you DON'T read a book you're told to read, you're already saying it loud and clear. Some people have patience or just don't care. Silverman does, and you're too sensitive to look past the abrasion and actually TAKE GOOD ADVICE.

Instead of following through with expert information given to you, you decide instead to hang out with someone who CLEARLY has no clue what the hell is going on, has paranoid delusions and shit-for-math.

Finally, stop using your mental illness as a crutch. EVERYONE on this board knows that your education was cut short because of your mental illness. You mention it almost every third post. GET OVER IT. I have plenty of friends who have mental illness issues, and they do fine in mathematics. Hell, look at John Nash.

Stop apologizing for being an amateur and then getting offended when you get treated like one. Stop apologizing for not knowing the requisite material and GO LEARN THE REQUISITE MATERIAL. You've been repeatedly told where to find it. Yes, it's hard. No, it's not glorious. Sometimes it's very dull, unexciting work. But everyone who helps you has gone through it, and I loathe people who want to abuse the knowledge of others to try and take a shortcut. You have to put in the work.

[ewmayer]

Tough Love claims another victim...

BTW, who is this "Hilter" fellow jasong seems to dislike so much? Is he a famous mathematician - perhaps a distant name-mangled relative of Hilbert? Does he have a function space named after him? You know, as in

"Hilter space ... the final frontier..."

I can see how that kind of math credibility on the late Mr. Hilter's part would make the jasong's of this world intensely resentful.

Originally Posted by jasong

If you wish to know how my trials go with testing (2^3355584+1)/769, you may inquire at Riesel Sieve Forum in a week or two. I fully expect to discover that 769 DOESN'T divide the number.

By way of a postscript, allow me to spare the folks here the "suspense" of waiting breathlessly for the results of Jasong's "trials" of his alleged prime:

Question: Does 769 divide (2^3355584+1)?

Answer: Exponent 3355584 = 1100110011001111000000 in base 2. To check divisibility by 769, use the LR exponentiation algorithm to obtain 2^3355584 modulo 769, then add 1 to the result:

iteration    bit  x % 769 ("residue")
---------    ---  --------------------
0            1    2
1            1    2*x^2 =   8, % 769 =   8
2            0      x^2 =  64, % 769 =  64
3            0      x^2 =4096, % 769 = 251 (from here on just show the modded result)
4            1    2*x^2 % 769 = 655
5            1    2*x^2 % 769 = 615
6            0      x^2 % 769 = 646
7            0      x^2 % 769 = 518
8            1    2*x^2 % 769 = 655
9            1    2*x^2 % 769 = 615
10           0      x^2 % 769 = 646
11           0      x^2 % 769 = 518
12           1    2*x^2 % 769 = 655
13           1    2*x^2 % 769 = 615
14           1    2*x^2 % 769 = 523
15           1    2*x^2 % 769 = 299
16           0      x^2 % 769 = 197
17           0      x^2 % 769 = 359
18           0      x^2 % 769 = 458
19           0      x^2 % 769 = 596
20           0      x^2 % 769 = 707
21           0      x^2 % 769 = 768

Add one to get 769, which == 0 modulo 769, hence 769 divides (2^3355584+1). A child could do it - if it weren't a whiny, petulant unwilling to listen and learn, that is.

And Jason, what you "discover" with respect to the above divisibility problem matters not one whit, since the above PROVES that 769 is a divisor. Not "possibly shows," not, "is likely effective", but PROVES - do you even have a clue as to what that means? Wait, don't answer that if it means you coming back to here to waste more of our time and the forum's bandwidth.

[retina]

http://en.wikipedia.org/wiki/Conspiracy_theory

[xilman]

Originally Posted by ewmayer

BTW, who is this "Hilter" fellow jasong seems to dislike so much?

He was a candidate in the North Minehead by-election in the 1970's.

I'm surprised jasong has even heard of him. He (jasong) clearly has a better education than I'd surmised from his postings here.


Paul

[axn]

<wild speculation>
Considering the original post's emphasis on 10-million digit prime, I am just wondering may be the intended number is F25 = 2^2^25+1 = 2^33554432+1. It looks similar, is over 10m digits, and is at least a non-trivial candidate (except for the fact that it has three known factors)
</wild speculation>

[ewmayer]

Originally Posted by xilman

He was a candidate in the North Minehead by-election in the 1970's.

Ah yes, it's all coming back to me now - I seem to recall a Green theme to his candidacy - no buses and electronic equipment for the campaign staff, just bicycles and bullhorns. IIRC he was doing surprisingly well in the polls [given that no one could understand what he was saying in his impenetrable German accent] until some bizarre-but-innocent proposal he floated to the effect of every Dutchman deserving a living room was misheard and promptly sound-bited as "Jedem Deutschen sein Lebensraum", which led to a rather unfortunate comparison with a near-namesake of 40 years earlier being drawn. Poor bloke - he meant well, he just wasn't good at public-image shaping. Of course much of blame for that falls on the shoulders of his feckless campaign coordinator, Ron Vibbentrop.

"Oh well, you'll want the A39 then...no, no, you've got the wrong map there, this is Stalingrad, you want the Ilfracombe and Barnstaple section."

[paulunderwood]

Originally Posted by ewmayer

Question: Does 769 divide (2^3355584+1)?

Answer: Exponent 3355584 = 1100110011001111000000 in base 2. To check divisibility by 769, use the LR exponentiation algorithm to obtain 2^3355584 modulo 769, then add 1 to the result:

iteration    bit  x % 769 ("residue")
---------    ---  --------------------
0            1    2
1            1    2*x^2 =   8, % 769 =   8
2            0      x^2 =  64, % 769 =  64
3            0      x^2 =4096, % 769 = 251 (from here on just show the modded result)
4            1    2*x^2 % 769 = 655
5            1    2*x^2 % 769 = 615
6            0      x^2 % 769 = 646
7            0      x^2 % 769 = 518
8            1    2*x^2 % 769 = 655
9            1    2*x^2 % 769 = 615
10           0      x^2 % 769 = 646
11           0      x^2 % 769 = 518
12           1    2*x^2 % 769 = 655
13           1    2*x^2 % 769 = 615
14           1    2*x^2 % 769 = 523
15           1    2*x^2 % 769 = 299
16           0      x^2 % 769 = 197
17           0      x^2 % 769 = 359
18           0      x^2 % 769 = 458
19           0      x^2 % 769 = 596
20           0      x^2 % 769 = 707
21           0      x^2 % 769 = 768

Add one to get 769, which == 0 modulo 769, hence 769 divides (2^3355584+1). A child could do it - if it weren't a whiny, petulant unwilling to listen and learn, that is.

Using Fermat's little theorem:
2^768==1 (mod 769)
So 2^3355584+1 (mod 769) becomes:
2^(768*N+192) +1 (mod 769) for some N
2^(768*N)*2^192+1 (mod 769)
(2^(678))^N*2^192+1 (mod 769)
(1)^N*2^192+1 (mod 769) using Fermat's little theorem
2^192+1 (mod 769)

We know 2^768-1 is factored as (2^384+1)*(2^192+1)*(2^192-1) by recursive use of the difference of two squares: A prime "p=4*n+1" could divide (2^n+1).

192 in binary is 10100010 and could govern a 7-step version of Ernst's algorithm.

Is Pierre at Intel?