Fun with Numbers: The PanPrimeDigit Cube Hypothesis

08072017, 07:09 PM
(This post was last modified: 08082017 09:14 PM by David Hayden.)
Post: #15




RE: Fun with Numbers: The PanPrimeDigit Cube Hypothesis
(08072017 10:50 AM)AlexFekken Wrote: there are some obvious ways to cut down the number of required calculations quite a bit, as compared to a naive brute force attack. E.g. you could calculate the number of different values of n^3 mod 1000 (and then mod 10^6, then mod 10^9) that only contain the required digits. I would expect that that could narrow down the search quite a bit... [ Edit: I mistakenly thought that both the number N and the cube N^3 had to be panprimedigital. In reality only N^3 must be. The description below reflects my misunderstanding. The basic approach can still be applied to the problem though.] That's the approach I took last night with a C++ program and BigInt library. Multiplying two numbers with N least significant digits will result in the N least significant digits in the product, regardless of what the more significant digits are. So if you start with the panprimedigits and cube them. You find that for any number N ending in 2, N^3 will end in 8, so it can't be a panprimedigital cube. Thus any panprimedigit cube must end in 3, 5, or 7. Next you prepend 2, 3, 5, and 7 to these suffixes and test them. Here you find that any panprimedigit cube must end in 25, 33, 25, 37, 53, 55, 75 or 77. The program repeats the process until there are no more suffixes. I hoped that the number would eventually shrink. Boy was I wrong. My program ran all night. When I stopped it, it was checking 10 million+ 35digit suffixes and hadn't found a solution yet. I was running it on a slowish computer at work. I'll try running it on my laptop which has more horsepower. Joe can you confirm that the answer you found is more than 35 digits? 

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