Say someone decides to see if he can calculate the private key related to my adress he found on some Blockexplorer... What can I do against this?

You do nothing but they probably start watching this video at some point:

bitcoin_beginners

Someone calculated a fitting private key to my sole Bitcoin-adress 

Fabs

> Say someone decides to see if he can calculate the private key related to my adress he found on some Blockexplorer... What can I do against this?

You do nothing but they probably start watching this video at some point:

https://www.youtube.com/watch?v=S9JGmA5_unY

[Bitcoin uses the secp256k1 curve which uses 256-bit keys](https://en.bitcoin.it/wiki/Elliptic_Curve_Digital_Signature_Algorithm) 