5,7,11,13 are prime
I would suggest looking into the sieve of erasthenes for further reading.
For tests, look at odd numbers and see if odd numbers divide them. ie 9 is not in the lsit because it is divisible by 3. Even numbers are always divisible by two.
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The first five prime numbers between 100 and 200 are: 101 103 107 109 113.
Five: 41,43,47,53,59.
There are five prime numbers: 31, 37, 41, 43, and 47.
There are five prime numbers between 45 and 70: 47 53 59 61 67.
Twenty five.