The Quickest: I did it in about 15 minutes because there was a abandoned mineshaft showing from a crater, but I hesitated to approach it (this was when I was a horrible monster fighter) There was a Chest right when you got into the mineshaft with 2 diamonds in it.
The Longest: Currently I have a survival world I am working on that I am not doing very much mining. I did find 2 dungeons and made xp farms out of those and I am working on an epic base. Time in world so far: 2-4 hours. Diamonds: 0
Around an hour last time, although it took longer than usual because I had to mine down ~190 blocks (380 blocks mined as a 1x2 tunnel straight down, also needed three stacks of ladders). One at the bottom though I can find diamonds in 5-10 minutes, immediately upgrading to a diamond pickaxe as soon as I find some (you'll find more diamonds than you use even without Unbreaking, I also mine further down than most people).
Of course, once while testing one of my cave mods (in Creative) I followed a cave down to bedrock and found diamonds right away, a minute or two after spawn (nothing beats spawning in a village with diamonds though, but it doesn't really count unless you get the diamonds achievement).
Whenever I end up feeling like it... I don't see the rush, even in my world where I have put like 100 hours into i'm not even sure I have actually mined any diamonds yet. xD Just found a diamond pick in a jungle temple ages ago.
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'All we have to decide is what to do with the time that is given to us.' - Gandalf the Grey
Maybe my second day or something. I usually mine down from my first night's noob hole to pass the time. I get to level 12 and see if I can get a diamond sword before morning. Iron's more valuable to me though. Best case scenario is I find a deep-ass cave to do some caving for whatever goodies I can get.
If you mean from the moment the world is created, then it will be most likely be more than 4 hours. I like to make my base and set every possible farm I can get my hands on first before going on the search for Diamonds and/or mine shafts.
I've got one world with zillions of hours and builds on it, and I don't think I've ever mined for diamonds. I don't even wear armor in that game. And its on hard.
Try mining over 40,000 ore from caving* in a couple days of gameplay with unenchanted iron pickaxes; nothing beats an Efficiency V diamond pickaxe** (with Fortune) in mining efficiency (well, Haste makes it even faster, but probably too fast).
Not to mention, take a look at this chart (% diamond vs. % iron at diamond level), then look at this table (durability of diamond vs. durability of iron), then consider that Fortune III gives you about 2.2x more diamond, but not 2.2x more iron.
*Here's a map of the caves I've explored so far; I've also used 17,000 torches to light them up and have gotten over a stack of diamond blocks (over 200 diamond pickaxes, able to mine over 300,000 blocks, over 1.2 million with Unbreaking III; I also mined about 10,000 stone for about 50,000 total blocks mined, so that's a 24:1 ratio of diamonds found:diamonds needed for pickaxes; of course, with Fortune III and Unbreaking III, but still practical even with unenchanted pickaxes, including mining diamond ore without Fortune, around 3:1):
**Of course in my current main world I use amethyst armor/tools that are better than diamond (5000 durability for tools, Eff V diamond mining speed, though adding Eff makes them too powerful and also too expensive to repair, costing 37 levels for a one-unit repair of a Fortune III Unbreaking III pickaxe). Also, so far I've found about 16 times as much diamond as amethyst while caving, to give you an idea of how rare it is - yet I have more than enough for repairing (I even made it rarer in my current world, previously the ratio was around 8:1, I still use only about half of what I find for repair).
The quickest was 10-15 minutes. Usually I don't play 24/7 but I play a couple hours per day. So I would say around a week of how long I play Minecraft. (Not counting all the hours together, just counting the days I played atleast for a hour or more)
I don't usually look specifically for diamonds and do many things other than mining, so it generally takes quite a while for me to find any diamonds.
It usually takes a few days before I find any diamonds. It is usually when one of my mining tunnels has reached its target depth and I have started actively digging the column mine for that tunnel. Even then, I'm usually looking for redstone rather than diamonds since I usually need more redstone than diamonds.
That being said, I do keep finding diamonds in mind when digging at those depths and when I do explore caves (which I don't do very often), I am often hoping to find diamonds deep in the cave.
I guess I'm not the kind of person who immediately looks for diamonds. I just find them when I find them, really.
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The source of my intention isn't really crime prevention; my intention is prevention of the lie! Yeah, welcome to the Scatman's world!