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A positive number is called n-primable if it is divisible by n and each of its digits is a one-digit prime number. How many 3-primable positive integers are there that are less than 1000?

 Apr 9, 2020
 #1
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The only one-digit prime numbers are 2, 3, 5, and 7.

To be divisible by 3, the sum must be divisible by 3.

We get 222, 333, 555, and 777.

Also 225, 237, 255, and 357.

[Plus other combinations of these numbers.]

 Apr 9, 2020
 #2
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I count 64 such numbers as follows:

 

222  223  225  227  232  233  235  237  252  253  255  257  272  273  275  277  322  323  325  327  332  333  335  337  352  353  355  357  372  373  375  377  522  523  525  527  532  533  535  537  552  553  555  557  572  573  575  577  722  723  725  727  732  733  735  737  752  753  755  757  772  773  775  777  Total =  64

 Apr 9, 2020

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