Edit:
Example of a strange public key:
0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c633f3979bf72ae8202983dc989aec7f2ff2ed91bdd69ce02fc0700ca100e59ddf3
0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63c0c686408d517dfd67c2367651380d00d126e4229631fd03f8ff35eef1a61e3c
Find their difference, also after that check 69 and 96 as hex, convert them to decimal and compare their values and difference in values, as I have said before this is an ocean, and somehow the designers of EC and the math involved either used magic to come up with these equations, or I am still unable to fathom the infrastructure underneath them all, yet. Do not rely on existing tools, if you can come up with new solutions, share them if they can not be used to endanger coins other than puzzle coins. Otherwise you should not reveal anything if it can be exploited to steal coins from people.
That's bullshit mate. These are freaking completely normal
VALID public keys and have of course private keys that are connected to the them. There is nothing strange with them or what so ever....
Just because a public key has many zeros does not make it "weird" or "strange".
Here's a
VALID private key with many zeros. Is it weird?
000000000000000000000000000000000ffff000000000001111111111100000
It's actually interesting to see public keys that follow this pattern. The keys produce the following addresses when the are uncompressed:
at compressed format they produce the following addresses (and they had an out transaction meaning they have a valid private key)