Originally posted by AThousandYoung What's so important about the number 137? There's a small hint at the bottom of this post.
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Hint: It has to do with chemistry and physics.

It is prime! Further, it is a Twin Prime (139 is also prime) and, subsequently, a Chen Prime.

Originally posted by AThousandYoung That's what I was looking for.

Why is 138 not classically stable?

Apparently the fine structure constant is approximately 137.036, which figures into the following expression for classical (non-relativistic) electron speed:

v = Z*c/137.036

where Z is the atomic number of the element. When Z = 137, the speed is still slightly less than the speed of light, but if Z = 138 or more, the speed becomes superluminal. When you take relativistic effects into consideration, apparently 138 becomes OK too.

Originally posted by PBE6 Apparently the fine structure constant is approximately 137.036, which figures into the following expression for classical (non-relativistic) electron speed:

v = Z*c/137.036

where Z is the atomic number of the element. When Z = 137, the speed is still slightly less than the speed of light, but if Z = 138 or more, the speed becomes superluminal. When you ...[text shortened]... s into consideration, apparently 138 becomes OK too.