I am super happy that my classmate Yen, who happens to work at ITP as well, heard about my project and gave me a beautiful big natural stone that he kept in his office . Very likely it is granite and therefore a good source for natural radiation / random numbers.
So last night I sat down and did a few experiments measuring the amount of decaying particles with and without a stone close to the geiger-counter. I conducted 3 test rows, so three times with the stone, three times without the stone.
Here are the results measured over the time of 3 minutes each: