These steps can reduce our work:
First of all we will write all the even numbers between 89 and 97: 90, 92, 94 & 96.
Then multiples of 5: 90 & 95.
Multiples of 3: 90, 93 & 96 and also the multiple of 7 which is 91.
There is no other number left between 89 & 97.
Therefore, numbers between 89 & 97 are all composite numbers.
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90 ( 3 x 30)
91 = (7 x 13)
92 = ( 2 x 46)
93 = ( 3 x 31)
94 = ( 2 x 47)
95 = ( 5 x 19)
96 = 8 x 12)
All of them except for 83, 89 and 97 which are prime numbers
The numbers 83, 89 and 97 are prime.
They are: 90 91 92 93 94 95 and 96 which are between the prime numbers of 89 and 97
95 A composite number has a factor in addition to 1 and itself, so it is not a prime number. 11, 47, 89 and 97 are all prime numbers. 95 is divisible by 5 and 19 in addition to 1 and itself - so 95 is the composite.
89 and 97