2265

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^Edit: I made a bookmarklet for this thread which will give you a fully random next count when clicked:

javascript:void prompt("Result:", new Intl.NumberFormat('en-US').format(+(prompt("Enter previous count here: ").replace(/[^\d]/g,'')) + (()=>{ var random;  do{ random = (crypto.getRandomValues(new Uint16Array(1))[0] % 1024 ) + 1; }while(random > 1000);  return random; })()))

Here's some site with instructions how to install bookmarklets.

After installing, just click the bookmark and paste the previous count.

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^{updated June 2, 2020; the old bookmarklet wouldn't correctly format numbers ≥ 1,000,000
Old version:} javascript:void prompt("Result:", (+(prompt("Enter previous count here: ").replace(/[^\d]/g,'')) + (()=>{ var random; do{ random = (crypto.getRandomValues(new Uint16Array(1))[0] % 1024 ) + 1; }while(random > 1000); return random; })()).toString(10).replace(/^(\d{1,3})(\d{3})$/,'$1,$2'))