# Can the prime $619$ ever be the least prime factor 0f f(n)?

Let f(n)=$1234567891011$...n (i.e. concatenating the first n integers). And consider this sequence of numbers n:

• 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....

So we have this sequence : $2,3,25,43,157,19,271,229,49,31,181,91,397,481,301,127,511,439,2701,37,79,253,793,1531,1237,523,1867,637$. My question : What is the smallest value of n such that $619$ is the least prime factor of f(n)?

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