# Materials used in metallic glass

I've been looking over the lists of materials used together to make metallic glass.

Is it purely coincidental that if you round up/down any decimals from the atomic weight of elements used to construct metallic glass, you're always very close to +-1 (if not at) a prime number for the atomic weight of each element?

Yes, it’s coincidental. There is no expectation that prime (or near-prime) atomic weight means anything for the element itself. In fact, your affirmation is not even true: on the list given by Wikipedia, the first two examples are:

• $\ce{Au_75 Si_25}$, your assertion is true
• “an alloy of 77.5% palladium, 6% copper, and 16.5% silicon”, and your assertion isn’t met for copper

Let's go further. For a given element, how likely is it that its atomic weight, rounded, is within ±1 of a prime number? Well, atomic weights are relatively low integers, and prime numbers are plenty numerous among small integers, so it is relatively frequent. The answer can be computed with Mathematica:

weights = {#, Round@ElementData[#, "AtomicWeight"]} & /@ ElementData[All];
f[i_] := PrimeQ[i] || PrimeQ[i - 1] || PrimeQ[i + 1]
res = {f[#[[2]]], #[[1]]} & /@ weights
Select[res, ! #[[1]] &][[All, 2]]


74 out of the first 118 elements turn out to satisfy your “near-prime atomic weight” condition, which is 63%. This seems high, but it's not: if you do the same check, not only for atomic weights, but for all integers below 200, 61% of them are near-prime:

Total@Boole@Select[f /@ Range[1, 200], # &]

• Thank you for your time. I have learned two things. First it's just coincidental. Second, and more importantly, I have a long way to go in my own fact checking. Thank you for identifying my discrepancy. The third one is that an unbelievably high number of elements are near-prime in their atomic weight (statistically speaking). That's kind of cool. – Everett Sep 29 '12 at 15:28
• @Everett it's not such much that many atomic weights are “near-prime”, that many small integers are near-prime. I’ve updated the end of my answer to clarify that… – F'x Sep 29 '12 at 20:38