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?


1 Answer 1


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], # &]
  • $\begingroup$ 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. $\endgroup$
    – Everett
    Commented Sep 29, 2012 at 15:28
  • $\begingroup$ @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… $\endgroup$
    – F'x
    Commented Sep 29, 2012 at 20:38

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