Random number from a range in a Bash Script
According to the bash man page, $RANDOM is distributed between 0 and 32767; that is, it is an unsigned 15-bit value. Assuming $RANDOM is uniformly distributed, you can create a uniformly-distributed unsigned 30-bit integer as follows:
$(((RANDOM<<15)|RANDOM))Since your range is not a power of 2, a simple modulo operation will only almost give you a uniform distribution, but with a 30-bit input range and a less-than-16-bit output range, as you have in your case, this should really be close enough:
PORT=$(( ((RANDOM<<15)|RANDOM) % 63001 + 2000 ))