Filter on last digit of long number

I'm trying to filter documents on the last digit of a long number field called file.mode to find world writable files.

I would like to do something like this regex query file.mode:/0..[2367]/
So filter documents where the last digit of file.mode is either 2,3,6 or 7

Any ideas?

The last digit of a long is returned by the modulo 10. You can make use of that fact in a script query:

GET my_index/_search
{
  "query": {
    "script": {
      "script": {
        "source": "long modulo = doc['file.mode'].value % 10; for (value in params.values) { if (value == modulo) return true; } return false",
        "params": {
          "values": [
            2,
            3,
            6,
            7
          ]
        }
      }
    }
  }
}

Script queries are not always going to be very performant. If you plan to use this query often, you are better off with indexing the modulo 10 as a separate field in your documents. That will allow you to query that field without the need for any scripting.