53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 . . .
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That's an infinite list, started by 53.
The prime numbers between 31 and 50 are 37,41,43,47.
The numbers 53, 59, 61 and 67 are prime.
The prime numbers between 30 and 50 are 31,43,39,41, and 47
prime numbers between 50 and 60: 53 & 59