First, a public address is not the key you are looking for, it is the hash of the key. So, if you ever did find a key pair that hashes to a certain address there is a chance that with all your efforts you end up with the wrong key pair.
Second, by too long we mean the following:
Here are some estimates for generating some addresses using just my laptop. You can extrapolate to a faster system, even a GPU system or even 100,000 GPUs and see that it is “impossible”:
Exact pattern Time
1 found 1HszrwReND62cBZUBZhqLTPKxAoSsANuxK instantly
12 found 12UpCienamnaM8Vw8pdTEFJ39Mth23CK3N instantly
123 found 123r9SzaKwgZF6xjit3Svs1jTU8TWitrcn instantly
1234 found 1234Ru7M2a6HHXpr5sE31n7TdgSTXcREen instantly
12345 found 12345RDRciJmSBywxSGTJSHYrvAr4xBVUH in about 30 seconds
123456 about 30 minutes
1234567 about 1.2 days
12345678 about 70 days
123456789 about 11 years
123456789a about 640 years
123456789ab over 36,000 years
123456789abc over 2 million years
123456789abcd over 100 million years
123456789abcde over 7 billion years
123456789abcdef over 400 billion years
123456789abcdefg over 20 trillion years
123456789abcdefgh over 1 quadrillion years
From above you can kind see that it would take a “long” time to find a key pair that generates any one public address.
In fact the vanitygen program will not calculate how long it would take (too large) but to just get most of one (which does not get you the coins) here is the output from the program showing that you have a 50% chance of finding only most of one in 6e32 years:
C:\downloads\www.bitcoin.org>vanitygen 1LJY4ey9FVKKuodaDr84sdZDXLy
Difficulty: 2794725737275825531787289201741966674434639341
[102.98 Kkey/s][total 1497088][Prob 0.0%][50% in 5.965101e+032y]