Question 1006479
The single digit prime numbers are: 2,3,5,7


There are 4*3*2 = 12*2 = 24 different ways to select 3 numbers from the list of 4 primes shown above.


Here is the list of all of the possible 3 digit numbers we can form


235
237
253
257
273
275
325
327
352
357
372
375
523
527
532
537
572
573
723
725
732
735
752
753


Notice there are 24 numbers in the list above.


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Now let's toss out the composite (aka non-prime) numbers


235 is not prime because 5 is a factor ( 5*47 = 235)
237 is not prime because 3 is a factor ( 3*79 = 237)
253 is not prime because 11 is a factor ( 11*23 = 253)
273 is not prime because 3 is a factor ( 3*91 = 273)
275 is not prime because 5 is a factor ( 5*55 = 275)
325 is not prime because 5 is a factor ( 5*65 = 325)
327 is not prime because 3 is a factor ( 3*109 = 327)
352 is not prime because 2 is a factor ( 2*176 = 352)
357 is not prime because 3 is a factor ( 3*119 = 357)
372 is not prime because 2 is a factor ( 2*186 = 372)
375 is not prime because 3 is a factor ( 3*125 = 375)
527 is not prime because 17 is a factor ( 17*31 = 527)
532 is not prime because 2 is a factor ( 2*266 = 532)
537 is not prime because 3 is a factor ( 3*179 = 537)
572 is not prime because 2 is a factor ( 2*286 = 572)
573 is not prime because 3 is a factor ( 3*191 = 573)
723 is not prime because 3 is a factor ( 3*241 = 723)
725 is not prime because 5 is a factor ( 5*145 = 725)
732 is not prime because 2 is a factor ( 2*366 = 732)
735 is not prime because 3 is a factor ( 3*245 = 735)
752 is not prime because 2 is a factor ( 2*376 = 752)
753 is not prime because 3 is a factor ( 3*251 = 753)



Those numbers listed above are tossed out of the list. The only numbers left are 257 and 523


The only prime numbers of that 24 item list are
257
523


There are only 2 such numbers that have these characteristics
a) the number is 3 digits
b) each digit is a prime number
c) each digit is unique/different
d) the number is prime



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Question: How many three digit primes have all three digits as different primes?


Answer: 2