#PowerShell, 35 Bytes
param($a)$a-match'^(?!(..+)\1+$)..' Uses the same regex from Martin's Retina answer, as that's way shorter than anything that will wind up using the [math]:: libraries one would normally use. Expects input as command-line argument in unary format.
Corrected from initial version (which was apparently specific to the particular PowerShell implementation I coded it on) thanks to Jonathan Leech-Pepin. Grr undocumented version differences.
Examples:
PS C:\Tools\Scripts\golfing> .\is-this-number-a-prime.ps1 111111 False PS C:\Tools\Scripts\golfing> .\is-this-number-a-prime.ps1 1111111 True ###Bonus - PowerShell pipeline input, 29 Bytes
%{$_-match'^(?!(..+)\1+$)..'} Same as the above, just called differently, which shaves bytes. For example,
PS C:\Tools\Scripts\golfing> 111111 | %{$_-match'^(?!(..+)\1+$)..'} False