I found myself a good observation which gives the result as - no integer from the sequence 111,1111,11111,.... is a prime number. Can anyone prove this ? (My observation can be wrong as well , then you can disprove it).
Such numbers are known as repunits. A repunit with (n) digits is denoted by (R_n). It is known that (R_n) is a prime for (n=2,19,23,317)and 1031. (Source : Wikipedia).
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