# Why is tellurium-128 so stable compared to the other radioisotopes?

Tellurium-128 is the longest lived radioisotope so far with a half-life of 2.3 septillion ($$2.3*10^{24}$$) years. I know I've heard something about so called "magic numbers" that if you have the perfect amount of protons and neutrons in an atomic nucleus it usually is radioactive but has an absurdly long half-life (examples bismuth-209,xenon-124). But why is tellurium-128 this stable? And why is this for the ones I have just said?

Magic numbers of protons and neutrons have no role in this. Well, I mean, they are related to the same field: if a nucleus has either of these, or better both, it is expected to be more stable than its peers. $$\rm^{128}Te$$ doesn't and isn't.
If anything, $$\rm^{128}Te$$ is (or was; I didn't check) a temporary winner in a perpetual race. In due time, longer half-lifes will be detected, and then longer yet, and so on.