In search of proof

 Attempted to set up a test of the randomness of the Conjecture on Excel.

1)  Set up a sheet with 250,000 cells, each containing 4 digits of the PRS formatted as a 4-character text string (i.e. 1 million digits).

 

2)  Set up a second sheet with a table 100 deep by 100 wide and enabled each cell to do a 'countif' enquiry on table 1, thus establishing the distribution of all the possible 4-digit 'words' in table 1.

 

3)  Selectively formatted sheet 2 so as to spot the outliers and zoomed out so I could see all of it.

4)  Hit F9 and ... all 16 processors on the server scratched their collective heads for 01:20 and produced this (with the exception of 0000 and 9999 things seem pretty random - when the server workload is light will run again and post graphics):