Fun with Numbers: The PanPrimeDigit Cube Hypothesis

07302017, 06:17 AM
Post: #1




Fun with Numbers: The PanPrimeDigit Cube Hypothesis
A "panprimedigit number" is a natural number containing all four prime digits (2, 3, 5, and 7) in any order, one or more times each, but no other digits. The smallest panprimedigit number is 2357, which also happens to be a prime number, but there are obviously infinitely many panprimedigit numbers, and probably infinitely many prime ones. I'm pretty sure that the smallest panprimedigit number which is a perfect SQUARE is 23377225 (equal to 4835^2). There are probably infinitely many panprimedigit squares.
However, it is my hypothesis that there is ONLY ONE panprimedigit CUBE. I would be delighted beyond words if anybody could either prove (mathematically) or disprove (by counterexample) this hypothesis. Needless to say, finding the one known panprimedigit cube is left as a mini programming challenge. This posting appears in the "Not remotely" forum because no current HP programmable calculator is fast enough to find the number in a reasonable amount of time; it's surprisingly large. <0ΙΈ0> Joe 

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