To be a whole number of centimetres, the number of inches must be a multiple of 50. For the number of centimetres to be even, the number of inches can be further narrowed down to multiples of 100. For both the number of inches and the number of centimetres to avoid being one more than a multiple of 3, the number of inches must be a multiple of 300. This straight away narrows down the task to the point where we can check individual cases.

If the number of inches were 2100, that would convert to 5334cm: 2099, 5333 and 7433 are all prime.

So the distance is 2100 inches or 5334 cm.

This is the only possible distance under 200m as the next set of numbers that fit the criteria are: 9000 inches (22860cm).