Between 89 and 97, both of which are prime numbers, there are 7 composite numbers,

90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90

91 = 1, 7, 13, and 91

92 = 1, 2, 4, 23, 46, and 92

93 = 1, 3, 31 and 93

94 = 1, 2, 47, and 94

95 = 1, 5, 19 and 95

96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96