Consider the following:

66 65 28 27 06 05 00 01 14 15 44 45 91

67 64 29 26 07 04 03 02 13 16 43 46 90

68 63 30 25 08 09 10 11 12 17 42 47 88

69 62 31 24 23 22 21 20 19 18 41 48 87

70 61 32 33 34 35 36 37 38 39 40 49 86

71 60 59 58 57 56 55 54 53 52 51 50 85

72 73 74 75 76 77 78 79 80 81 82 83 84

When you count up by 0,1,2,3..., you get a serpentine pattern. If you notice, there's a series of triangle numbers below the zero and the remainder of the triangle numbers embedded in the first row.

What other patterns can you find? What can you say (if anything) about the prime numbers?