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I have partitioned the chemical elements into two groups based on a certain property that is shared by some of them, but not by the remaining ones.

The following elements have my enigmatic property:

Bismuth, Chlorine, Gold, Helium, Iodine, Mendelevium, Nitrogen, Silver

The following elements do not have my enigmatic property:

Dubnium, Erbium, Nobelium, Terbium, Ytterbium, Yttrium, Zinc, Zirconium

Which of the following elements do have this property?

Aluminium, Fluorine, Francium, Gallium, Lutetium, Neon, Oxygen, Polonium.

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The property is

having a prime atomic number.

The first group:

Bismuth 83
Chlorine 17
Gold 79
Helium 2
Iodine 53
Mendelevium 101
Nitrogen 7
Silver 47
All of these atomic numbers are prime.

The second group:

Dubnium 105 (divisible by 5)
Erbium 68 (divisible by 2)
Nobelium 102 (divisible by 2)
Terbium 65 (divisible by 5)
Ytterbium 70 (divisible by 5)
Yttrium 39 (divisible by 3)
Zinc 30 (divisible by 5)
Zirconium 40 (divisible by 5)
None of these atomic numbers are prime.

Therefore, of the final group:

Aluminum 13 (prime)
Fluorine 9 (divisible by 3)
Francium 87 (divisible by 3)
Gallium 31 (prime)
Lutetium 71 (prime)
Neon 10 (divisible by 5)
Oxygen 8 (divisible by 2)
Polonium 84 (divisible by 2)
Aluminum, Gallium, and Lutetium have the property.

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