Definition: f(n) = 10^(n-1) + 10^(n-2) + ... + 10¹ + 10⁰
Or: f(n) = ((10ⁿ) -1)/9

f(2) = 11
f(3) = 3 * 37
f(4) = 11 * 101 = f(2) * 101
f(5) = 41 * 271
f(6) = 111 * 1001 = 11 * 10101 = f(3) * f(2) * 7 * 13
f(7) = 239 * 4649
f(8) = f(4) * 73 * 137
f(9) = f(3) * 3 * 333,667
f(10) = f(5) * f(2) * 9091
f(11) = 21649 * 513,239
f(12) = f(4) * f(3) * 7 * 13 * 9901
f(13) = 53 * 79 * 265,371,653
f(14) = f(7) * f(2) * 909,091
f(15) = f(5) * f(3) * 31 * 2,906,161
f(16) = f(8) * 17 * 5,882,353
f(17) = 2,071,723 * 5,363,222,357
f(18) = f(9) * f(2) * 7 * 13 * 19 * 52,579
f(19) = 1111111111111111111
f(20) = f(10) * 101 * 3541 * 27961
f(21) = f(7) * f(3) * 43 * 1933 * 10,838,689
f(22) = f(11) * f(2) * 11 * 23 * 4093 * 8779
f(23) = 11111111111111111111111
f(24) = f(12) * 73 * 137 * 99,990,001
f(25) = f(5) * 21401 * 25601 * 182,521,213,001
f(26) = f(13) * f(2) * 859 * 1,058,313,049
f(27) = f(9) * 3 * 757 * 440,334,654,777,631

F(2), F(19), and f(23) are prime.
Next potential prime = f(59)