Prime counting
Number Theory
Level
2
There are exactly different 9-digit numbers where every digit form 1 to 9 appears. How many primes are there in this set of numbers?
The answer is 0.
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1 solution
There are no 9-digit primes consisting of all of the digits from 1 to 9, because the sum of those digits is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 4 5 , meaning that every such number must be divisible by both 9 and 3 , making them all composite.