I want to rename multiple files in the same directory using Bash scripting. Names of the files are as follows:

file2602201409853.p
file0901201437404.p  
file0901201438761.p  
file1003201410069.p  
file2602201410180.p

I want to rename to the following format:

file2503201409853.p
file2503201437404.p  
file2503201438761.p  
file2503201410069.p  
file2503201410180.p

I was reading about the rename command, and try to do it this way, but it does nothing, I think I have questions about the syntax. Then I read that you can make a loop using the mv command as follows:

for file in cmpsms*2014*.p; do
    mv "$file" "${file/cmpsms*2014*.p/cmpsms25032014*.p}"
done

But I can not rename the files. What am I doing wrong?