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 Feb 22 revised How many different numbers can be written if each used digit symbol is used at least 2 times? added 23 characters in body Feb 22 revised How many different numbers can be written if each used digit symbol is used at least 2 times? added 23 characters in body Feb 22 revised How many different numbers can be written if each used digit symbol is used at least 2 times? deleted 934 characters in body Feb 22 revised How many different numbers can be written if each used digit symbol is used at least 2 times? added 1 character in body Feb 22 revised How many different numbers can be written if each used digit symbol is used at least 2 times? added 1 character in body Feb 22 revised How many different numbers can be written if each used digit symbol is used at least 2 times? added 9 characters in body Feb 22 revised How many different numbers can be written if each used digit symbol is used at least 2 times? added 272 characters in body Feb 22 revised How many different numbers can be written if each used digit symbol is used at least 2 times? added 147 characters in body Feb 22 revised How many different numbers can be written if each used digit symbol is used at least 2 times? added 1590 characters in body Feb 21 revised How many different numbers can be written if each used digit symbol is used at least 2 times? edited body Feb 21 revised How many different numbers can be written if each used digit symbol is used at least 2 times? deleted 66 characters in body Feb 21 revised How many different numbers can be written if each used digit symbol is used at least 2 times? added 656 characters in body Feb 21 revised How many different numbers can be written if each used digit symbol is used at least 2 times? added 34 characters in body Feb 21 revised How many different numbers can be written if each used digit symbol is used at least 2 times? added 34 characters in body Feb 21 awarded Nice Question Feb 21 revised How many different numbers can be written if each used digit symbol is used at least 2 times? added 62 characters in body Feb 21 revised How many different numbers can be written if each used digit symbol is used at least 2 times? added 9 characters in body Feb 21 comment How many different numbers can be written if each used digit symbol is used at least 2 times? @MarkusScheuner : I believe that $P(n,d)$ function can be a key function to detect prime numbers. It has wonderful features Feb 21 comment How many different numbers can be written if each used digit symbol is used at least 2 times? Your answer is great. Have you read my conjecture : $n^{d}\equiv P(n,d) \pmod {d}$ , I have not found any counter-example yet. It satisfies for any number in your table but I do not know how to prove it .Thanks for helps. Feb 21 comment How many different numbers can be written if each used digit symbol is used at least 2 times? :Thanks a lot for answer . I edited my question with wonderful discover for $P(n,d)$. Could you please share your comments on my last edit?