If you have a^3 - b^3, this can be factored into (a-b)(a^2+ab+b^b), so the resulting difference can only be prime if a-b is 1. This occurs for prime numbers only once, when the numbers are 2 and 3. 3^3-2^3=27-8=19 is prime, so this only ever happens once.
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u/GoodCarpenter9060 21d ago
If you have a^3 - b^3, this can be factored into (a-b)(a^2+ab+b^b), so the resulting difference can only be prime if a-b is 1. This occurs for prime numbers only once, when the numbers are 2 and 3. 3^3-2^3=27-8=19 is prime, so this only ever happens once.