I've had my fill of ones....

In 1918, Oscar Hoppe proved that 1.111.111.111.111.111.111 (19 ones) is indeed a prime number. From these, we MAY deduce that ones with a prime numbers of digit is a prime, is this true? For example, let's try finding the primes in: 2 ones, 3 ones, 5 ones, and so forth until 17 ones (prime ones under 19). How many of them are indeed prime numbers?

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