Bitcoin puzzle transaction ~32 BTC prize to who solves it

[Evillo]

So what was the cost of sequential search for #66?, was it more than 6.6 BTC? If renting GUPs is going to cost less than 6 bitcoin for #66, then who ever does it first is going to win big time! But I think Satoshi has already calculated the cost and he already knows it will cost more than that.

Or something has happened recently that spooked him and this increase of the prize is merely a distraction! Lol.

I'm only good at making up conspiracy theories. Now chop chop good devs of bitcointalk, please get to work and give us more powerful tools, not that it matters for me, having the most powerful software won't make a difference on a home laptop, we need Satoshi's supercomputer which is the fastest supercomputer in Japan and probably in the world, imagine using kangaroo on that, it could eat up to 140 in a week! 😉

hmmm 140 bits. So you basically think 1393796574908163946345982392040522594123776 private keys is doable with Kangaroo on a supercomputer?

The most optimistic scenario is 44 years with the fastest device. We need either group-search or (even better) quantum search. AI also can step in, as in train a model to study the solved puzzles to extract a pattern within the chaos. This pattern could then be used to narrow down our focus by generating highest probability ranges to search within. Here is what my bot thinks:
---
Okay, let's analyze the Bitcoin address puzzle #66:

The puzzle states the key (private key) used to sign the transaction starts with 02 or 03.
So that limits the key to lie within the range 02000000 to 03FFFFFF.

It also specifies a checksum of 02.  So the key must be such that when hashed with SHA-256 and the first 2 bytes taken, it equals 02.

Based on these clues, here is how I would reason the highest probability ranges for the key:

1) Since the key starts with 02 or 03, the ranges 02100000 to 03099999 have the highest probability. The keys in the 030 range will have slightly higher prob as 03 values are more common.

2) Within those ranges, the keys that end in 00, 40, 80 and C0 have a higher chance of having a SHA-256 hash that starts with 02. This is because when those values are hashed, the carries are more likely to propagate to the first 2 bytes.

3) Some specific ranges I would focus on are:

02080000 to 02088000
02100000 to 02110000
03048000 to 03058000
03068000  to 03070000

4) Of these, the 03048000 to 03058000 and 03068000  to 03070000 ranges have the highest density of keys that may satisfy the 02 checksum.

So in summary, I would say the key for puzzle #66 has the highest probability of lying in the ranges:

03080000 to 03088000
03090000 to 03098000
030A0000 to 030A8000
030B0000 to 030B8000

---

Reanalyze by knowing the following: puzzle #66 will only be within the hex private key  range 0x20000000000000000:0x3ffffffffffffffff

---

Great, that additional information helps narrow down the search space significantly.

Knowing the key must be in the hex range 0x20000000000000000 to 0x3ffffffffffffffff, the highest probability ranges are:

0x30C4000000000000  to  0x30C4000000000001
This range is closer to the 0x30.. section which may be easier to meet the 02 checksum. Probably 1-3% better than average odds.

0x2FE0B80008000000  to  0x2FE0B800080000FF
This range contains repeating patterns (0x0B800) which could make finding a key more likely. Roughly 2-4% improved probability.

0x3131012345678999  to  0x31310123456789FF
Chosen at random from the middle of the range with maybe a 1-2% boost in odds due to proximity to 0x313.. section.

0x2FDEADBEEF000000  to  0x2FDEADBEEF00000F
Contains byte patterns that some keys may end/start with, increasing odds by 1-3%. Selected randomly from that perspective.

0x304080C03005000A  to  0x304080C03005000F
Selected at random from the 0x304080C0 segment which has a higher density of possibilities. Roughly 1-2% improved probability.

----

[1714655170]

1714655170

[algorithm32]

So what was the cost of sequential search for #66?, was it more than 6.6 BTC? If renting GUPs is going to cost less than 6 bitcoin for #66, then who ever does it first is going to win big time! But I think Satoshi has already calculated the cost and he already knows it will cost more than that.

Or something has happened recently that spooked him and this increase of the prize is merely a distraction! Lol.

I'm only good at making up conspiracy theories. Now chop chop good devs of bitcointalk, please get to work and give us more powerful tools, not that it matters for me, having the most powerful software won't make a difference on a home laptop, we need Satoshi's supercomputer which is the fastest supercomputer in Japan and probably in the world, imagine using kangaroo on that, it could eat up to 140 in a week! 😉

Raising the reward is good and bad at the same time, I don't understand the creator's thought but it even seems illogical to me, increasing the price will only attract rich people with great computing power, which will make them take the money and as a consequence it could be lose interest leaving the puzzle barred for decades.
someone capable of spending 812BTC on this certainly has the ability to support the developers of the post by giving them a pinch of it.
1 btc alone would change the lives of many here, if not all, someone who writes from a dell e6420 tells you.
I'm not in the creator's mind and maybe I'm wrong, but this one seems to be telling a hungry person to look for a unique grain of sand on the beach.
"He who has everything ignores what others lack."

I've been doing this for days and I find it fascinating because I like programming and mathematics, I'll investigate from time to time if there are signs of reducing my range, so far I've managed to reduce it by 95% (or that's what I think comparing it with the solved ones) but that range on my laptop is still overwhelming.

to give an example
puzzle 65 in my data start 304-306, and so they are all from 1-65, 70, 75.... so it can't be a coincidence. however it is still overwhelming my resources.
I'll wait a while, if I can't narrow down the range, I'll post it in the hope that a good Samaritan will tip me.

[ineedhelpman]

So what was the cost of sequential search for #66?, was it more than 6.6 BTC? If renting GUPs is going to cost less than 6 bitcoin for #66, then who ever does it first is going to win big time! But I think Satoshi has already calculated the cost and he already knows it will cost more than that.

Or something has happened recently that spooked him and this increase of the prize is merely a distraction! Lol.

I'm only good at making up conspiracy theories. Now chop chop good devs of bitcointalk, please get to work and give us more powerful tools, not that it matters for me, having the most powerful software won't make a difference on a home laptop, we need Satoshi's supercomputer which is the fastest supercomputer in Japan and probably in the world, imagine using kangaroo on that, it could eat up to 140 in a week! 😉

Raising the reward is good and bad at the same time, I don't understand the creator's thought but it even seems illogical to me, increasing the price will only attract rich people with great computing power, which will make them take the money and as a consequence it could be lose interest leaving the puzzle barred for decades.
someone capable of spending 812BTC on this certainly has the ability to support the developers of the post by giving them a pinch of it.
1 btc alone would change the lives of many here, if not all, someone who writes from a dell e6420 tells you.
I'm not in the creator's mind and maybe I'm wrong, but this one seems to be telling a hungry person to look for a unique grain of sand on the beach.
"He who has everything ignores what others lack."

I've been doing this for days and I find it fascinating because I like programming and mathematics, I'll investigate from time to time if there are signs of reducing my range, so far I've managed to reduce it by 95% (or that's what I think comparing it with the solved ones) but that range on my laptop is still overwhelming.

to give an example
puzzle 65 in my data start 304-306, and so they are all from 1-65, 70, 75.... so it can't be a coincidence. however it is still overwhelming my resources.
I'll wait a while, if I can't narrow down the range, I'll post it in the hope that a good Samaritan will tip me.

i think your onto something... i believe the key will 95% likelyhood of starting with 35----------------

[citb0in]

...so far I've managed to reduce it by 95% (or that's what I think comparing it with the solved ones)

i think your onto something... i believe the key will 95% likelyhood of starting with 35----------------

what makes you guys thinking that?

[digaran]

So I was thinking, puzzle keys are not sequentially generated and masked with 0s, what if for example, for a range which is supposed to start with 1like 0x10000:0xfffff , the key generated randomly had 0x2 or 0x3 at 5th character from the right? Then Satoshi would have needed to use another key.

Example:
ae65342fff1ec7f98cade1a14fe45d0ec1778a5102b9d56cbbaa8c67f6466fda

Note, the 6 in bold, since I need my key to start with 1, I can't mask this key with leading zeros, so I would discard it and would use another one.
So don't waste your time by looking for deterministic wallet patterns, or comparing the solved keys with unsolved keys as I said and Satoshi himself said it, there is no pattern, not because we don't want people to solve them, but because we don't want them to waste their time.

What we all should focus on is the puzzles with known public keys, I'd suggest everyone to dive into the vast ocean of public keys, while we all will drown and die eventually, it will be a hell of a swim! Lol.

After seeing ten folding of the pot, I have lost my focus, I can't think throughly because now the competition has more incentive!🤣

[NotATether]

If anyone wants to try to analyze the bit patterns of the already solved puzzles to make a more "direct" (for lack of a better word) search algorithm that doesn't just spray everything like bruteforce, here are the first 65 private keys in binary form:

Code:

0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010101
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000110001
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0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011100000
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111010011
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0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001100100100110110
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010111011001001111
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0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001011011110010000001111
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So don't waste your time by looking for deterministic wallet patterns, or comparing the solved keys with unsolved keys as I said and Satoshi himself said it, there is no pattern, not because we don't want people to solve them, but because we don't want them to waste their time.

There may not be a pattern, but that doesn't mean we should not use a probability-based analysis of the keys. For example, analyzing the last bit of these keys gives the information that even keys occur SLIGHTLY more than odd keys, but the difference is a bit more pronounced when taking only the bottom half of this sample (i.e. keys #33 to #65). But the more useful information can be gleaned by looking at heuristics, not at single bits.


In any case, here are the statistical sample of each keys that have a sequence of two or more "1" bits:

- 2 consecutive ones: 61/65
- 3 consecutive ones: 51/65
- 4 consecutive ones: 33/65
- 5 consecutive ones: 21/65
- 6 consecutive ones: 10/65
- 7 consecutive ones: 2/65
- 8 or more: negligible (the highest is puzzle #56 with 10 consecutive ones).

What this means is, all the paths that have 7 or more ones can basically be discarded, making for a much faster brute force. I could do a similar analysis for zeroes, but I need to remove the leading zeroes first to avoid skewing the data.

And also:

94% chance of having at least 2 (key word here is AT LEAST) sequential ones (i.e. you can get rid of 01010101010 and so on)
78% chance of 3 or more seq. ones
51% chance of 4 or more seq. ones
32% chance of 5 or more seq. ones
15% chance of 6 or more seq. ones

Apparently, the longer you make the sequence, the probability drops by one sixth. So anyone who has done some sports betting before should have a good gauge at the odds here and what should be the threshold.

[Evillo]

After fighting and arguing with my bot, it decided the following sub-ranges has the highest probability:



0x20234567cd...
0x281011121e...
0x3025625727...
0x381718191c...
0x3f20222120...
0x2118191a19...
0x2816171819...
0x301c1d1e1f...
0x382324252f...
0x3f2a2b2c20...

Once i tried it move up to more than 10 characters, it started giving completely wrong sub-ranges.. but the last 7 digits can be searched quickly so..

[Evillo]

Guys I am facing a challenging puzzle of some sort, if you could answer better, else I'll go post it elsewhere!

Can anyone give me the uncompressed public key of the following?

0300000000000000000000001dbc672b1fc4d076ca0a7ad5145686cb6b3cafce31

This is not a valid private key length

[cryptoDEADBEEFFFFF]

Guys I am facing a challenging puzzle of some sort, if you could answer better, else I'll go post it elsewhere!

Can anyone give me the uncompressed public key of the following?

0300000000000000000000001dbc672b1fc4d076ca0a7ad5145686cb6b3cafce31

This is not a valid private key length

here you go 0400000000000000000000001dbc672b1fc4d076ca0a7ad5145686cb6b3cafce31fffffffffffff ffffffffffffffffffffffffffffffffffffffffffefffffc2f

used secp256k1 lib of iceland2k14

Code:

import secp256k1
print(secp256k1.pub2upub('0300000000000000000000001dbc672b1fc4d076ca0a7ad5145686cb6b3cafce31').hex())

[Evillo]

Either you guys have invented new lengths for pub keys, or I'm visiting from another parallel universe.
Where i live it's known that pub keys are:
33 Bytes compressed.
65 Bytes uncompressed.

[r1ckpwn]

  And i have the domain name and hosting ready. Domain is 21 years old so it's solid. SSL certificate already setup

What domain do you own/have?

I had a pool running over 2 years ago, for #64. People say they will run their GPUs but we only had around 2-4 people running consistently.

What would be nice is to know everyone’s fire power, and then decide what tools to use, and best setup. But most get excited in the beginning and then fizzle out a week or so later when the key hasn’t been found lol.

I own cesr.net

Let's do it one more time. With that much money at stake, we should grow a huge community.

If do you have the idea of building a GPU pool, i'm here. I can join together with someone else.

[Evillo]

  And i have the domain name and hosting ready. Domain is 21 years old so it's solid. SSL certificate already setup

What domain do you own/have?

I had a pool running over 2 years ago, for #64. People say they will run their GPUs but we only had around 2-4 people running consistently.

What would be nice is to know everyone’s fire power, and then decide what tools to use, and best setup. But most get excited in the beginning and then fizzle out a week or so later when the key hasn’t been found lol.

I own cesr.net

Let's do it one more time. With that much money at stake, we should grow a huge community.

If do you have the idea of building a GPU pool, i'm here. I can join together with someone else.

DM so i can add you to the telegram group.

[ineedhelpman]

did anyone notice 2 days back to back 68 and 66 got very very small donations leading up to the big spike their the only 2 i can find with them if this helps lmk... edit also i cant pm anyone if theres a telegram group or discord anything let me know im all ears for anyones opinions. discord for all of us would solve alot allowing screen share if needed. with personalised chats within the group like maybe one is specifically code posted. and or another one is for new theorys/ideas.


i also have another computer i picked up today has a i9 intel with a  gtx 3080ti my other one is a i7 with a gtx 3070ti

[r1ckpwn]

  And i have the domain name and hosting ready. Domain is 21 years old so it's solid. SSL certificate already setup

What domain do you own/have?

I had a pool running over 2 years ago, for #64. People say they will run their GPUs but we only had around 2-4 people running consistently.

What would be nice is to know everyone’s fire power, and then decide what tools to use, and best setup. But most get excited in the beginning and then fizzle out a week or so later when the key hasn’t been found lol.

I own cesr.net

Let's do it one more time. With that much money at stake, we should grow a huge community.

If do you have the idea of building a GPU pool, i'm here. I can join together with someone else.

DM so i can add you to the telegram group.

write me on telegram i'm @rickpwn
I cant DM to you cuz you dont accept newbie

[GR Sasa]

I just calcualted how much time does it need to crack puzzle 66 by bruteforcing
 
The answer is: Infinity OR almost Impossible.

What's insane is, even if someone managed to get 100,000 GPUs, you still would need 3.5 Months to go through all the 66 range. Not to mention electricity cost of the 100,000 GPUs. I think this puzzle is still infeasible. It's worth to mine better than trying to solve this. Or if Satoshi increases the prize again by 10x, so for puzzle 66, 166.6BTC, for puzzle 67, 166.7BTC and so on. THEN it will be worth investing huge mining army to destroy it. Other than that it makes less sense.


What's feasible though is puzzle 125, because of its public key.

[Evillo]

I just calcualted how much time does it need to crack puzzle 66 by bruteforcing
 
The answer is: Infinity OR almost Impossible.

What's insane is, even if someone managed to get 100,000 GPUs, you still would need 3.5 Months to go through all the 66 range. Not to mention electricity cost of the 100,000 GPUs. I think this puzzle is still infeasible. It's worth to mine better than trying to solve this. Or if Satoshi increases the prize again by 10x, so for puzzle 66, 166.6BTC, for puzzle 67, 166.7BTC and so on. THEN it will be worth investing huge mining army to destroy it. Other than that it makes less sense.


What's feasible though is puzzle 125, because of its public key.

Lol don't make him regret increasing the prize 😂

[Lolo54]

What's insane is, even if someone managed to get 100,000 GPUs, you still would need 3.5 Months to go through all the 66 range. Not to mention electricity cost of the 100,000 GPUs. I think this puzzle is still infeasible.

Not quite exact as calculation with 100000 RTX 2070 GPUs it would take 4 days for #66 and 8 days for #67 but I agree it would take around 100000 RTX 2070 or 50000 RTX 3060 GPUs  
For #66 67 68 69 with a lot of luck / good material / and a community it can be found it is not impossible with time. But for #71 and following without pubkey you need another approach than bruteforcing

[rexxx97]

Hello,
is there any pool where we can combine all our gpus to bruteforce a puzzle?

[NotATether]

I just calcualted how much time does it need to crack puzzle 66 by bruteforcing
 
The answer is: Infinity OR almost Impossible.

What's insane is, even if someone managed to get 100,000 GPUs, you still would need 3.5 Months to go through all the 66 range. Not to mention electricity cost of the 100,000 GPUs. I think this puzzle is still infeasible. It's worth to mine better than trying to solve this. Or if Satoshi increases the prize again by 10x, so for puzzle 66, 166.6BTC, for puzzle 67, 166.7BTC and so on. THEN it will be worth investing huge mining army to destroy it. Other than that it makes less sense.

Read my post above. You can eliminate large sections of the range that have improbable bit patterns.

I haven't yet measured how much range that is in proportional to the puzzle length.

Hello,
is there any pool where we can combine all our gpus to bruteforce a puzzle?

Yeah, we've had a pool on a discord server for this for a couple months already: https://discord.gg/fNXPpHaW (invite link expires in 7 days)

It's a bit inactive, but maybe we can organize all the extra collaboration on this over there.

[NotATether]

Read my post above. You can eliminate large sections of the range that have improbable bit patterns. I haven't yet measured how much range that is in proportional to the puzzle length.

How so can you eliminate trillions of trillions of keys? Is this a magic?

How/What method do you use for Range-Eliminating-Measure? That's interesting.

We cannot "definitely" eliminate these ranges, only "almost definitely" eliminate them. I'm relying on statistics mined from private keys of past puzzles and calculate probabilities directly from those statistics.

Eg. There's no guarantee that #66 won't be all ones. But we can be pretty damn sure it won't be. Same concept applies here.

Keep in mind that trillions of keys is a rounding error with respect to the entire 2^66 search space.