<p>The time between two blocks, assuming the hashrate and difficulty match, follows an <a href="https://en.wikipedia.org/wiki/Exponential_distribution" rel="nofollow noreferrer">exponential distribution</a> with mean 10 minutes.</p>
<p>The distribution has:</p>
<ul>
<li>a mean of 10 minutes (600 seconds)</li>
<li>a median of 6 minutes and 56 seconds (<em>600/ln(2)</em> seconds).</li>
</ul>
<p>The difference between the two is due to the long tail the distribution has: while 50% of blocks will be shorter than ~7 minutes, and 50% will be longer, the longer ones are spread out over a much larger range (up to infinity, even), driving the average up.</p>

CC BY-SA 4.0
2024-12-30T20:56:41.617Z
Thank you! Could you please point me to any resource explaining the details of the exponential distribution with a mean of 10? I am mainly looking for mathematical proof to know if there is a mathematical basis or if it is primarily based on an accepted consensus.
Dr. Strangelove
CC BY-SA 4.0
2024-12-30T21:07:50.650Z
This is trivial to prove, and can readily be computed: https://www.wolframalpha.com/input?i=median+of+exponential+distribution+with+lambda%3D1%2F600 ?
Pieter Wuille
CC BY-SA 4.0
2024-12-30T21:14:31.997Z
That makes sense! Thanks! I wonder if there are any sources explaining why we think it follows the exponential/Poisson distribution. I found quite a few posts about how those distributions work, but it is unclear why we believe it follows those distributions.
Dr. Strangelove
CC BY-SA 4.0
2024-12-30T21:20:24.083Z
It is a Poisson process (https://en.wikipedia.org/wiki/Poisson_point_process), which follows from the fact that every hashing attempt is independent. The time between events in a Poisson process is exponentially distributed.
Pieter Wuille
CC BY-SA 4.0
2024-12-30T21:23:00.263Z
Is there any reference for "The time between events in a Poisson process is exponentially distributed"?
Dr. Strangelove
CC BY-SA 4.0
2024-12-30T20:45:27.073Z
2024-12-30T20:45:27.073Z
Pieter Wuille
<p>When I check the <code>time</code> or <code>mediantime</code> fields recorded in bitcoin blocks, the delta between consecutive blocks is rarely the commonly known 10 min interval.</p>
<p>For instance,</p>
<pre><code>Block   Median Time     Delta
------  -----------     -----
299996  1399700280
299997  1399700940      660
299998  1399700975      35
299999  1399701277      302
300000  1399701278      1
</code></pre>
<p>I am looking for references diving deep into mathematical proof of the differences.</p>

CC BY-SA 4.0
2024-12-30T20:15:39.183Z
This question is similar to: [Why can the block production rate be as low as two per hour?](https://bitcoin.stackexchange.com/questions/106878/why-can-the-block-production-rate-be-as-low-as-two-per-hour). If you believe it’s different, please [edit] the question, make it clear how it’s different and/or how the answers on that question are not helpful for your problem.
RedGrittyBrick
CC BY-SA 4.0
2024-12-30T20:30:19.267Z
There are a few similar topics on this site already, e.g., [Why was the time between these two blocks not approximately 10 minutes?](https://bitcoin.stackexchange.com/q/16609/5406), [What keeps the average block time at 10 minutes?](https://bitcoin.stackexchange.com/q/855/5406), and [What is the expected time until the next block is found?](https://bitcoin.stackexchange.com/q/3909/5406). Does any of these answer your question? If not, could you please clarify how your question is different?
Murch
<timestamp><block-interval>
The "one block roughly every 10 min" does not match the median time stamp of consecutive blocks
Dr. Strangelove
# The "one block roughly every 10 min" does not match the median time stamp of consecutive blocks

(Asked by: username_0 on 2024-12-30)

When I check the `time` or `mediantime` fields recorded in bitcoin blocks, the delta between consecutive blocks is rarely the commonly known 10 min interval.

For instance,

```
Block   Median Time     Delta
------  -----------     -----
299996  1399700280
299997  1399700940      660
299998  1399700975      35
299999  1399701277      302
300000  1399701278      1

```

I am looking for references diving deep into mathematical proof of the differences.

**Tags:** timestamp, block-interval

> **Comments:**
> **username_1**: This question is similar to: [Why can the block production rate be as low as two per hour?](https://bitcoin.stackexchange.com/questions/106878/why-can-the-block-production-rate-be-as-low-as-two-per-hour). If you believe it’s different, please [edit] the question, make it clear how it’s different and/or how the answers on that question are not helpful for your problem.  
> **username_2**: There are a few similar topics on this site already, e.g., [Why was the time between these two blocks not approximately 10 minutes?](https://bitcoin.stackexchange.com/q/16609/5406), [What keeps the average block time at 10 minutes?](https://bitcoin.stackexchange.com/q/855/5406), and [What is the expected time until the next block is found?](https://bitcoin.stackexchange.com/q/3909/5406). Does any of these answer your question? If not, could you please clarify how your question is different?  

---

## 1 answers

### Answer by username_3 on 2024-12-30. Score: 2 | Accepted answer

The time between two blocks, assuming the hashrate and difficulty match, follows an [exponential distribution](https://en.wikipedia.org/wiki/Exponential_distribution) with mean 10 minutes.

The distribution has:

* a mean of 10 minutes (600 seconds)
* a median of 6 minutes and 56 seconds (*600/ln(2)* seconds).

The difference between the two is due to the long tail the distribution has: while 50% of blocks will be shorter than ~7 minutes, and 50% will be longer, the longer ones are spread out over a much larger range (up to infinity, even), driving the average up.

> **Comments:**
> **username_0**: Thank you! Could you please point me to any resource explaining the details of the exponential distribution with a mean of 10? I am mainly looking for mathematical proof to know if there is a mathematical basis or if it is primarily based on an accepted consensus.  
> **username_3**: This is trivial to prove, and can readily be computed: https://www.wolframalpha.com/input?i=median+of+exponential+distribution+with+lambda%3D1%2F600 ?  
> **username_0**: That makes sense! Thanks! I wonder if there are any sources explaining why we think it follows the exponential/Poisson distribution. I found quite a few posts about how those distributions work, but it is unclear why we believe it follows those distributions.  
> **username_3**: It is a Poisson process (https://en.wikipedia.org/wiki/Poisson_point_process), which follows from the fact that every hashing attempt is independent. The time between events in a Poisson process is exponentially distributed.  
> **username_0**: Is there any reference for "The time between events in a Poisson process is exponentially distributed"?  

---

