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| | An Analysis of Same-Atomic-Weight Isotopes |
 | | For example, if the atomic number and atomic weight are related by a simple fraction, there is usually a large preference (downward residual) (added stability for that isotope), while if either is a prime number, or if the two have no simple relationship, there is usually a strong negative preference (upward residual). |
 | | In certain (even atomic weight) isotope weight families, there is an (odd atomic number) isotope very near the center of the parabola which has an atomic weight that is higher than the adjacent even atomic number isotopes, because they each have an extra 2-symmetry preference (both even atomic weight and even atomic number). |
 | | Along this reasoning, if both the number of protons and the atomic weight is even, the nucleus would be especially stable for having a double symmetry, so much so that an isotope of equal atomic weight and atomic number either one higher or lower is generally unstable with beta decay. |
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