prove? No, it is indeed possible...
Each time you try, there is one chance in 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976 that you find the exact private key belonging to a certain address.
The main problem here is that human minds are not capable of comprehending such numbers...
Are you afraid of getting hit by lightning? Well those odds are 1 in 1,222,000 PER YEAR
Are you afraid of dying by being hit by a meteorite? Well those odds are 1 in 250,000 (in a lifetime)
source:
https://stacker.com/stories/2343/odds-50-random-events-happening-youIf you live, for example, 70 years, the odds of being hit by lightning and later in your life dying because you were hit by a meteorite are 1 in 4.357.142.857. So it's 335426605300057279761503315041820000000 times more likely to have those two things happen, than it is to guess an exact private key...
Now, offcourse, there are estimated to be around 460.000.000 funded addresses (
https://www.buybitcoinworldwide.com/how-many-bitcoin-users/). So, you have to divide 335426605300057279761503315041820000000 by 460.000.000 if you want to know how much the odds are compared to generating a private key for *any* funded address.
Then you end up with 729.188.272.391.428.869.046.746.337.047
Now, let's assume you're not generating one key, but you're able to generate 2002 Mk/s (
https://en.bitcoin.it/wiki/Vanitygen), this is grossly exaggerated, since this vanitygen program only generates keypairs, but does not do a lookup for unspent outputs funding those addresses.
Let's see how big the odds are that you can find *one* private key belonging to *one* funded address in a lifetime of 70 years compared to getting hit by lightning AND dying of an astroid:
729.188.272.391.428.869.046.746.337.047 / (2002.000.000 keys/second * 60 seconds * 60 minutes * 24 hours * 365 days * 70 years) =
729.188.272.391.428.869.046.746.337.047 / 4.419.455.040.000.000.000 =
164.995.065.181
CONCLUSION:
It is 167 billion times more likely to be hit by lightning AND dying from a meteorite strike than it is to run a GPU 24/7 generating address for 70 years and finding a single private key whose public key hash was once fundedI don't know about you... but i like those odds... Sure, they are not 0, they'll never be 0, but nothing in this life is absolute... I am very sure the odds of somebody impersonating you and stealing all your money from your bank account is much, much higher than somebody robbing you from your bitcoin... The odds of your bank vault being opened during a bank robbery and your gold being stolen is higher than the odds you get robbed out of your bitcoin... Hell, the odds of your country dissapearing and your money not being worth the paper it's printed on is much higher than your bitcoin being stolen.... At least, in a perfect world... In reality most people get robbed because they used a weak RNG, a vulnerable wallet, an infected pc, fall victim to phishing, fall victim to an evil maid,...