A cyclops number is a nonnegative integer whose decimal expansion has an odd number of digits and exactly one 0, in the central position. The 0 represents a single eye. The first examples are 0, 101, 102, 103, ..., 109, 201, ... (OEIS A134808). The nonzero digits on the two sides need not match: 109 is a cyclops number but not a palindromic number. The cyclops numbers that are prime begin 101, 103, 107, 109, 307, 401, ... (OEIS A134809).
The same definition can be used in an integer base 
, with no leading zeros. For 
digits
with 
,
there are 
possibilities, since each of the 
noncentral digits may be any of
the 
nonzero digits. The only one-digit case is 0.
In base 2, the noncentral digits must all be 1, so binary cyclops numbers are necessarily palindromic.
With 
ones on each side of the central 0, their values are
 |
giving 0, 5, 27, 119, 495, 2015, ... (OEIS A129868; Numberphile 2015). For 
both factors exceed 1, so these values are composite.
Since 
and 
,
the only binary cyclops prime number is 5.
