#PowerShell, 35 Bytes
param($a)$a-match'^(?!(..+)\1+$)..'
Uses the same regex from Martin's [Retina answer](https://codegolf.stackexchange.com/a/57618/42963), as that's way shorter than anything that will wind up using the `[math]::` libraries one would normally use. Expects input as command-line argument in unary format.
Corrected from initial version (which was apparently specific to the particular PowerShell implementation I coded it on) thanks to [Jonathan Leech-Pepin](https://codegolf.stackexchange.com/users/45925/jonathan-leech-pepin). Grr undocumented version differences.
Examples:
PS C:\Tools\Scripts\golfing> .\is-this-number-a-prime.ps1 111111
False
PS C:\Tools\Scripts\golfing> .\is-this-number-a-prime.ps1 1111111
True
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###Bonus - PowerShell pipeline input, 29 Bytes
%{$_-match'^(?!(..+)\1+$)..'}
Same as the above, just called differently, which shaves bytes. For example,
PS C:\Tools\Scripts\golfing> 111111 | %{$_-match'^(?!(..+)\1+$)..'}
False