Initially, looking at all four digit primes consisting of middle number pairs (e.g. -00-, -11-, -22- ... -99-) indicates a range of 10 to 13 possibilities for any given pair, well beyond my limited computing/spreadsheet skills to fully analyse (I eagerly await Charlie's full spin on the solution). One significant exception, however, is clearly **7 **as an __impossible__ value for 'x'.

There are only 6 such possibilities using -77- (i.e. 1777, 2777, 3779, 5779, 6779 and 8779). Note that each ends with either a 7 or 9 (with no 1's or 3's). That means each of the four squares in the __bottom__ row must therefore consist of either a 7 or a 9 only. There are, however, simply __no__ prime numbers consisting of just (7 or 9) (7 or 9) (7 or 9) (7 or 9), arranged in any combination. Ten primes therefore cannot be achieved with a grid having 7 as the value for 'x'.