Values of L_n, the length of the longest increasing subsequences in 4,000 random permutations on {1, 2, ..., n} for n = 10^10. There was 1 permutation in which L_n was 199791, 2 in which it was 199793, and so on. 1 199791 2 199793 1 199806 2 199808 2 199809 1 199811 1 199814 3 199815 1 199816 1 199817 1 199818 4 199819 1 199820 1 199821 4 199822 1 199823 2 199824 2 199826 2 199827 5 199828 3 199830 11 199831 3 199832 2 199833 5 199834 2 199835 4 199836 7 199837 4 199838 2 199839 7 199840 6 199841 11 199842 7 199843 4 199844 7 199845 10 199846 7 199847 6 199848 10 199849 11 199850 9 199851 8 199852 10 199853 11 199854 8 199855 14 199856 11 199857 14 199858 22 199859 19 199860 21 199861 14 199862 24 199863 21 199864 13 199865 20 199866 24 199867 29 199868 29 199869 13 199870 17 199871 22 199872 23 199873 23 199874 28 199875 29 199876 42 199877 33 199878 17 199879 26 199880 31 199881 29 199882 26 199883 35 199884 36 199885 17 199886 31 199887 45 199888 32 199889 33 199890 37 199891 33 199892 33 199893 30 199894 27 199895 40 199896 40 199897 30 199898 26 199899 31 199900 50 199901 29 199902 45 199903 36 199904 31 199905 55 199906 36 199907 58 199908 27 199909 34 199910 30 199911 31 199912 40 199913 57 199914 37 199915 34 199916 32 199917 42 199918 40 199919 41 199920 52 199921 33 199922 38 199923 45 199924 36 199925 37 199926 34 199927 23 199928 31 199929 36 199930 39 199931 24 199932 17 199933 40 199934 43 199935 30 199936 41 199937 28 199938 32 199939 31 199940 36 199941 40 199942 31 199943 26 199944 25 199945 38 199946 30 199947 26 199948 20 199949 23 199950 25 199951 16 199952 22 199953 22 199954 26 199955 23 199956 15 199957 24 199958 27 199959 28 199960 20 199961 24 199962 22 199963 12 199964 19 199965 13 199966 12 199967 7 199968 15 199969 23 199970 11 199971 12 199972 11 199973 14 199974 20 199975 17 199976 8 199977 6 199978 9 199979 13 199980 18 199981 14 199982 9 199983 8 199984 11 199985 8 199986 12 199987 12 199988 7 199989 9 199990 10 199991 6 199992 8 199993 10 199994 6 199995 5 199996 6 199997 7 199998 13 199999 8 200000 10 200001 10 200002 6 200003 6 200004 3 200005 4 200006 2 200007 4 200008 1 200009 3 200010 4 200011 7 200012 4 200013 1 200014 1 200016 9 200017 2 200018 1 200019 3 200021 2 200023 2 200024 3 200025 4 200026 3 200027 3 200028 3 200030 3 200031 1 200032 1 200033 1 200037 4 200040 3 200041 1 200042 1 200043 1 200044 1 200048 1 200050 2 200053 2 200063 1 200070