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?
+23246 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.]
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
