The problem with ^[1-9][0-9]{6}*$ is it is an invalid regex because of {6}* and ^([^0][0-9]){6}$ is that it is allowing any character that is not 0 followed by six digits.

Use

^[1-9][0-9]{5}$

Explanation:

1. ^: Starts with anchor


2. [1-9]: Matches exactly one digit from 1 to 9


3. [0-9]{5}: Matches exactly five digits in the inclusive range 0-9


4. $: Ends with anchor

Regex101 Playground

HTML5 Demo:

input:invalid {

  color: red;

}

<input type=text pattern=[1-9][0-9]{5} />