Changing your default(registered) mobile number at IRCTC is not easy.

Warning

Please do it only if you don't have any tickets which need cancellation in your account. There is a chance that you'll lose your account given IRCTC's bizarre software behaviors.

Steps

1. Login into your account
2. Click "Update Profile" under "User Profile" in your left menu:

   

3. Change your mobile and press "Update" button in the bottom of page:

   

4. You're now logged out with this message:

   

5. When logging again, you'll need to confirm your mobile number by entering the verification code:

   

If you were just trying with any random phone number then click the second link to change your mobile number and send the verification code to your new mobile number.