No it is not is ranges about $20.
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Technically no, you can create a mojang account for free but you won't be able to play minecraft Java.
go to mojang support center and look up in the bar above your screen "how to delete my mojang account"
Yes mineshaft was catched by Mojang is that why the mojang accounts are be created :( well If you have an old account in minecraft you can use it but If don't...
To log in to the game you use the same username and password you used to buy the game at the Minecraft website. If you have migrated your account to a Mojang account, use that email address and password.
Log onto your Mojang account and you will be able to request a password change. You may be asked an extra security question which you will have made when you created your account.