Any one here looking for a specific private key related to #125? You might have a lot of unknown public keys but you never know, someone  might know the private key for just one of them, and to solve the puzzle all we need is 3 keys, 2 known in order to find the third unknown one.

So if you have a few keys and would like to work together, post them here to see if we have what you need. I will start by myself.

If anyone knows the private key for any of the following keys, we will share the prize 50-50 😉.
This is not #125 key, it's a twin.
Another twin.
This one I have the private key for

Might post more later, lets see what you got, I showed you mine, it's your turn!😂

Just a simple dry please? Lol, here you can use key subtracter but it's not python.
https://bitcointalk.org/index.php?topic=5360656.msg57967989#msg57967989

But what you really need is an elliptic curve calculator, you should search in github, there are python written ones.

Incorrect, I can verify the keys or at least the one I'm working on is exactly in the said range, if you subtract for example 2^125 from puzzle #125, you will get a key #1, now if you subtract 2^124 from puzzle key, you will get key #2, and then if you add 1 and 2, you will get 2^124. I know the estimated size of any key related to that puzzle, the thing is, that estimation is as big as 2^123, but nevertheless you could verify the range as long as they tell you the range.

Over how many years exactly? 😂, #65 and #120 been solved. Prize has been increased 10 fold, now there is around 1000 bitcoins for us to loot ( yeah right).

It seems you know how to sing a lullaby, yet you can't sleep yourself. 😉
Only if it was so easy, though what could be faster than dividing or finding a divisor, is to figure out what comes after 1 for #125, I have worked on this for 2 months now, God willing if my calculations are correct, then I am 98% certain what comes next.

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If finding a single character of a low range key is so hard, imagine higher bit range keys, so I was wondering, now that I have managed to drop 2 digits from 32 digits of #125, how long would it take for kangaroo/BSGS to search in this new range which is a few times greater than 2^120?

I have a question, is it even possible to brute force a key  like puzzle #121? If it's possible I wonder what would be the cost?
And if the cost is more than the prize, no use, if the cost is less than the prize, again no use or purpose for designing this puzzle.

Think about it, revealing the exact range of every puzzle in order to see if people could brute force them while either the cost is more than the prize or less,  this doesn't make any sense and has no reasonable purpose honestly.

It wouldn't even prove anything, because it's obvious brute forcing keys especially 256 bit keys without known public key is impossible even if you know the estimated range as this challenge is the evidence.

So in my opinion working on any puzzle is a waste of time and effort if the prize is less than the cost, having a bigger prize than the cost of solving a key is also nonsense, because what? I have enough money and could use GPUs to solve a puzzle in order to earn something more than I have spent?
And if I have the money and calculate the cost to see it's not worth it, I would never attempt to solve a puzzle.

I think @Satoshi, or the actual designer of this puzzle should rethink and revise the purpose of this challenge.

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Imagine even if the whole world wanted to brute force a 256 bit key, they'd have to guess the range blindly and keep searching forever.

It would be nice to have unsolved puzzles above #67 moved to higher bit ranges with their public keys exposed, because I don't think there is any shortcut to solve a  key with no known public key other than brute forcing sequentially, though having a public key is at least something we could work with and improve on existing tools.
No public key = waste of time.

Ok,  maybe you are confused about the size  of the key range,  imagine a galaxy 10 billion years away from us,  now imagine there are no moving particles and everything standing still,  once again imagine you are given an option to pick any atom from the total existing atoms in the universe, now tell me in theory what are the odds of you landing on an atom in that far galaxy? How many times do you need to pick one key until you land on that one? You already know the answer, generate 2^256 keys one by one.

You need to sleep a bit more and think about the math a little more,  this is not good for your mind to insist on something which is not important at all, go back grinding for a puzzle key.😂

This is the public key of your private key
And this is the compressed address

You actually didn't break anything, you can't even control your generated address, when you generate a key, you are for the first time generating that key, unless you don't use secure RNG.
The only method to break ECC is through public keys, they are the only things connected mathematically to the private keys, since there are no identical public keys generated by different private keys.

You have not 1 in 2^160 odds, you actually have the entire 2^160 as your options to pick, you could either pick them all and store them somewhere, or you could generate as many needed to use.

If you generate an address without revealing the private key, now anyone else need to generate not in random, but sequentially from 1 up to 2^160 keys till they find your address, given you have chosen a 160 bit key, if you choose a 256 bit key, there is no specific range for others to search, so they'd need to search all 2^256 keys, and  if someone starts from 2^255.9 to 2^256,  he would still have the same odds as others searching sequentially.

Ps, almost all my math above is incorrect, I didn't calculate, just estimated.

Thanks, please do tell what you don't understand, I also need to go over stuff a few times to actually realize my mistakes and find inspiration, sometimes when I talk about something with someone, I'd suddenly realize something new.

I will do my best if I can to explain anything which is unclear for you.

You really think he just changed 1 digit? Some one who is an expert in cryptography would know better, but maybe he didn't want to make it very difficult and really used randomly generated keys. But if I were him, I'd have changed a few characters to make it really really hard, for example having a few 0s in a key will make it hard to reverse engineer a key manually, and brute force/kangaroo, well they have their limits.

One other thing could be placing a key outside a bit range, I'm curious did Satoshi ever confirmed that the keys are truly in the assumed bit ranges or we just hope the amounts of transactions are enough of a proof that the keys are exactly there?

But you know what I'd like to see? A large amount in a key with no exactly known bit range, somewhere between 160 and 180 bit not lower and not higher, then solving that key would be a global challenge, though not any amount which someone could spend half of it to use special tools and grab it, something which could only be solved by math and new methods.

For example, I haven't seen any tool/ algorithm capable of  adding or subtracting 1 to a key and then divide it by 2, kangaroo  engages square root calculations, BSGS looks for a match after adding/subtracting calculations, but no tool does + or - 1 then divide!

What do you mean the other half?  Of course spending money will do the trick of solving some of the puzzles, but as I said before, using high end hardware+ a lot of money to solve any of the puzzles is for dumb pussies, they wouldn't know any other way than spending cash to solve any problem they face.  Solving a puzzle by using the power of human mind is the ultimate honour one can achieve concerning this challenge.

And I don't know why so many people think that everything is in binaries, don't you know binary is the dictionary/vocabulary/language of computers? And math is the language of the universe and order, we humans do better with the things that were here before we existed, but trying to work with the things we created? Not a good idea, not only we can't learn anything from them, we'd become more dumb as many studies prove that human race is becoming dumber due to the excessive use of technology, lol. 
Imagine 50 years from now asking a 15 years old  what is 25 + 4? You would definitely see him reaching for his phone to use a calculator!

Good luck with -R flag, I assume that's  for random, only if people really knew how big a number like 2^125 is.😉

You should already know what is the right thing to do, asking people about it would just mislead you further.
In any case, anyone receiving any amount by mistake should post both receiving and sending addresses on social media, forums etc, to make it easier for the rightful owner to find you, then after making sure he/she controls the sending address, you should give him back all without taking 1 satoshi, the owner would give you a tip if he wants.

You might even want to ask him how much should you keep as a prize before returning them, and he might out of fear of loosing all of his coins tell you an amount which he is not satisfied to give whatsoever just to keep you happy and take some of his money back.

Doing something good has any worth if you do it with no expectation from people, God will make it up to you in a way that would result much better than doing good expecting something in return.😉

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Enough of ethical lessons, are you going to share some of that free loot or what? Come on man, this is a community ship, we share and care. Lol.

The topic is a hot bed for swarms of sig posters. 😉

I can't see any science in your theory, it's just a made up scenario in your head, I doubt him to be a liar, he said that he used a deterministic wallet to generate the keys.

The only thing I don't understand, are all the keys from one seed and if they are, did he use the first 256 keys and didn't generate more? If he used the first generated 256 keys, which would be impossible to generate 256 keys and all of them have the exact bit range of the intended bit range.

So my guess is that he might have used a single seed but had to generate more than 256 keys to find the perfect keys matching the intended bit ranges if masked with leading zeros.

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So explain what I mean.
Imagine I generate 256 keys and see none of them has 1 in the middle so that I could mask anything behind 1 with zeros and use that key for puzzle #125, for instance.

Example
I can't use the key above for puzzle #125 because it has 0 in the middle instead of 1, so I'd either  have to manually replace 0 with  1 or generate another key till I see 1 in the middle.

In both cases there will be no pattern, no correlation between the keys whatsoever.

Return of the jedi is more expected than the return of stolen crypto, I could save everyone 150 AED on how to keep your crypto safe, just use a cold wallet and you'd be Ok.
About unlocking an exchange account, if there is a misunderstanding, the user and the exchange will work it out, if it is related to regulations and laws of certain countries, then publicly teaching people how to circumvent the laws of a country is pretty much illegal, unless UAE, is an outlaw state, I don't see a good future for this meeting.😉

This is 2^125-1= 1fffffffffffffffffffffffffffffff you just need to add 1 to it.
I didn't have  this
cfbcda3ac10c9714fbcda3ac10c9700
I just used the distance key between #125 and 2^125  aka 
0286936a275e6d53bb2b2718c93d8a5aa44f371f6e0300abb73b89dd851d2fbe88
As my target and got this
0229ec62f37968906686bfad34ad5fdd9008fe187d868c0c4f9de1055b3062f00e

Then I did some subtractions to reach this  cfbcda3ac10c9714fbcda3ac10c9700
Those keys above are closer to #125 more than you think.

If we take 2^125 as number 20, I believe this key
0286936a275e6d53bb2b2718c93d8a5aa44f371f6e0300abb73b89dd851d2fbe88

Is somewhere around 5 and 6. I hope it helps you. I have been trying to find a way to force be88 and #125 to show up with anything other than  20000000000000000000000000000000  aka true 2^125. But instead I got a #125 counterpart ( look alike).😅

What is the story of 2000 BC in iran, do you have any sources and names to provide please?
Of course militaries use elliptic curves for encryption, but I doubt if they use a publicly available curve for that purpose. And maybe Satoshi didn't invent the ECDSA, secp256k1 curve, but he was smart enough to use it in order to secure bitcoin.

Secp256k1 is purely a safe vault, with other characteristics and utilities. Satoshi just chose to lock the door of the bitcoin vault using a locking mechanism we call secp256k1.

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Ps, I agree with you, I'm just a simpleton, doing simple stuff, saying simpler things.😉

So you used around 20GB of RAM  for this scan or am I reading it wrong? I wouldn't waste my time with findings based on similarity of addresses, just because a public key has a somewhat similar address to another key which we know is in 66 bit range doesn't mean the key of that address is in the same bit range.  There could be billions of such addresses in 2^255+ range, should you go and search there if we find a look a like address in those ranges?

If solving a puzzle was that easy by just comparing addresses with each other!!! More equipped people would have taken the coins long ago.  Actually lowering the bit range down to 66 bit is as difficult as solving DLP.

Though if you have spare resources, I could ask to go for a certain key whenever I am sure about it's exact range.😉

Thanks for the intel, I was under the impression that extracting anything related to the private key from a transaction or a signed message is not possible, or at least there is no useful data for extraction( cough, pooya, cough).

So indeed there is a way to find something out of a tx, or msg, it just goes back to the randomness and secure ways of generating private keys.

However, I would like to know, if it is possible to find something more about the private key from a tx than just having a public key? If there is, could I find something useful about a low range key such as a puzzle transaction challenge key with exposed public key?

Thanks again for your time and efforts to respond.

The laws of quantum physic are not applicable in the real world, and there is no space-time beyond the one universe we are in, there could be more in other dimensions which are hidden from our sight, but all the dimensions exist on the same plane of existence as we are. Things don't just come to existence randomly, everything was designed perfectly and the one God created the universe does not seem to do redundant and no use jobs, multiverse with different versions of us, or even with different creatures seems to have no practical use, since the one we are already in has more than enough space and resources to house trillion times more creatures than we could think of, but that is about another topic, this topic is about a new magical technology which only OP knows and cares about, a technology no one has ever heard of, just like some certain dead coin promoted by OP.

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But you could ignore the members you don't like to read, also what is there to discuss? A theoretical  future technology which does not exist, just like warp engines, or anti-matter fueled space ships, we could discuss day and night about countless of such future techs, while discussing about easier to reach techs like quantum computers and their applications is more productive.

However I apologize if I distracted you from having a decent conversation.

Some of my past works :

Wow, whoa, WHOAA!
Cool!
 

My team members resume :

Member number          their resume

1- Whoa, wow, WhOaA.
2- cool project.
3- cool story bro.
4- this is going to be interesting.
5- this is a gem.
6- I want to be on this rocket, destination moon! Wooohhhaaaa. (This team member is expensive than others due to longer comments).
7- I can't wait any longer.
8- my bags are full.
9- definitely going to moon.
10- this is so cheap, good for me!
11- watching this.
12- wow, whoa, WOW. ( you might wonder this is a second time, don't worry when we flood the thread with hundreds of comments, nobody would notice).
13- Guys I can tell this is a gem.
14- cool project bro. (Note the last one who said this didn't include "bro", so that counts as a totally different line).
15- buckle up people, moon here we come!
16- I smell scam. ( this is where we work on reverse psychology, it works like a charm, now look the next comment)
17- haters gonna hate! I see no scam here, if it was scam so many people wouldn't buy 99% of the ICO.
18- do you accept bank transfer?
19- this article from medium explains how a whale just bought $500 M ICO tokens using several identities, if the famous xxx invested $500 M on this, I'm certain about the success of this project.
20- seems scammy.
21- if it's a scam you are free to leave, let us buy this scam, I'll call you from moon soon!

The list of my team members is 10 times more than this, and I operate them all by myself, this is an expert band of shills, I am international actually.

This post just cost you $200, and $50 for each team member's comment, I give you 1 free to make your day! Now you need to pay up $1200, you can find my address in my profile,  I know a few Russian mobs, they have people all around the world, you either pay my $1200, or I will send them after you,  !!!! What? I can't hear you, did you really think if we work as shills to scam people, we wouldn't be willing to kill for money? This is on you,  you brought this upon yourself, now we will keep extorting you for the rest of your life! Lol in the order of the holy seven!