observed and predicted frequencies of occurrence of spacings for each k, gives GUE predictions for number of spacings out of 10^6 that fall into the interval ((k-1)/20, k/20], and the number actually observed for zeros of the zeta function in sets of 10^6, starting at zeros numbered about 1, 10^6, and 10^20, respectively k GUE N = 1 N = 10^6 N = 10^20 1 273.615 266 244 230 2 1902.381 1490 1646 1882 3 5095.719 4226 4296 5200 4 9726.649 7937 8438 9806 5 15606.739 13238 13608 15228 6 22486.726 19448 19972 21937 7 30057.609 26214 27093 29871 8 37954.941 34288 34612 37543 9 45769.565 42167 43416 45672 10 53067.199 50752 51256 52931 11 59417.289 57716 58083 59873 12 64428.815 64705 64075 64609 13 67788.278 70314 69712 67877 14 69293.525 72636 71662 69299 15 68877.038 73048 72123 68849 16 66613.885 72106 70661 66712 17 62712.271 66925 66715 62891 18 57487.956 61722 61073 58220 19 51326.765 54693 54115 51965 20 44641.384 47035 46881 44904 21 37829.194 38997 38879 37991 22 31237.095 31435 31738 31127 23 25137.324 24740 24939 25315 24 19715.927 19159 18936 19599 25 15073.199 14036 14165 15315 26 11233.630 10105 10394 11269 27 8161.959 7222 7250 7785 28 5781.740 4842 5020 5574 29 3993.374 3295 3421 3772 30 2689.453 2112 2270 2532 31 1766.255 1374 1373 1676 32 1131.173 794 867 1072 33 706.497 469 495 590 34 430.343 267 274 383 35 255.657 125 165 213 36 148.133 61 67 142 37 83.717 23 43 75 38 46.148 12 13 38 39 24.813 2 7 23 40 13.014 4 3 6