Are prime numbers really boring, though?
Define a positive integer to be boring if all the digits of the number are the same. How many positive integers less than are both prime and boring ?
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1 solution
The one-digit boring primes are 2 , 3 , 5 , and 7 .
The only two-digit boring prime is 1 1 , since 1 1 divides all other two-digit boring numbers.
No three-digit boring numbers are prime, since 1 1 1 divides all of them and 1 1 1 = 3 × 3 7 .
No four-digit boring numbers are prime since they are all divisible by 1 1 .
Therefore, there are 5 positive integers less than 1 0 0 0 0 which are both prime and boring .