When is the first case where $67$ is the least prime factor of f(n)?

Let f(n)=$1234567891011$....n

(concatenation of first n natural numbers). I make a sequence of numbers made with this following definition: Smallest number n such that the m-th prime number is the least prime factor/divisor of f(n). And I found these following:

• n=2 is the first case where 2 is the least prime factor of f(n)
• n=3 is the first case where 3 is the least prime factor of f(n)
• n=25 is the first case where 5 is the least prime factor of f(n)

• n=43 is the first case where 7 is the least prime factor of f(n)

• n=157 is the first case where 11 is the least prime factor of f(n)

• n=19 is the first case where 13 is the least prime factor of f(n)

• n=271 is the first case where 17 is the least prime factor of f(n)

• And so on...

• And quite far: n=793 is the first case where $83$ is the least prime factor of f(n)

My question: When is the first case where 67 is the least prime factor of f(n)? (Can 67 ever be the least prime factor of f(n)?). Additional question: Is there a prime number that will NEVER be the least prime divisor of f(n) ?

• Here are all solutions below $10^4.$ Commented Dec 9, 2015 at 20:15
• @Lucian, you mean all of them have least prime factor of 67 ? (thanks for that information!) : D Commented Dec 9, 2015 at 21:24