Elastic range query with range greater than a particular day of month

Question

I want to do a query using a range where in timestamp date is greater than , say 10th of the month (month in which query is being run) and less than now ( Time when query is being run) . I keep getting following exception when I run my query (snippet below)

"caused_by" : { "type" : "illegal_argument_exception", "reason" : "failed to parse date field [10d/d] with format [dd]", "caused_by" : { "type" : "date_time_parse_exception", "reason" : "date_time_parse_exception: Text '10d/d' could not be parsed, unparsed text found at index 2" }

GET /_search

{ "query": {

        "bool": {
          "filter": [
             {
              "range": {
                "@timestamp": {
                  "format": "dd", // I can't use MM in the format and in gte value as I want it to month and year agnostic 
                  "gte": "10d/d", 
                  "lt": "now" // The query run time, which will always be after 10th of every month
                }
              }
            },
            {
              "wildcard": {
                "kubernetes.namespace": {
                  "value": "apps-*-service"
                }
              }
            },
            
            {
              "term": {
                "level": {
                  "value": "WARN"
                }
              }
            },
            {
              "match": {
                "message": {
                  "query": "Some log text"
                }
              }
            }
          ]
        }

} }

I tried above code snippet and was expecting it to give me results by for the specified date range range. However it keeps giving parse error. Elastic version I am using is - 7.16.3