Do[ Print[ StringForm["Prime[``] = `` ", i, Prime[i]] ->

Do[
 Print[
  StringForm["Prime[``] = `` ", i, Prime[i]] -> (
    Count[FoldList[Plus, 1, GetCumulativePrimeSpacing[i]], _?PrimeQ]/
      Length[GetCumulativePrimeSpacing[i]]*1.
    )
  ], {i, 8}]

Prime[1] = 2 ->1.

Prime[2] = 3 ->1.

Prime[3] = 5 ->1.

Prime[4] = 7 ->0.895833

Prime[5] = 11 ->0.70625

Prime[6] = 13 ->0.562847

Prime[7] = 17 ->0.459245

Prime[8] = 19 ->0.389432‹