http://farm1.static.flickr.com/206/4763508_a2e6215b_m.jpg

Any Flickr picture URL has the following structure:
http://[farm].static.flickr.com/[server]/[photoID]_[secretCode]_[size].jpg
What follows is a real example of a Flickr Image [small size]
http://farm1.static.flickr.com/206/476361508_a2e625415b_m.jpg
From the above URL, the mail Flickr photo page will be located at the following location:
http://www.flickr.com/photos/476361508/ [476361508 is the PhotoID assigned by flickr.com]
To reconstruct other Flickr URLs pointing to different sizes of the same image, all we need to do is change the suffix as descibed here:
s for small square 75x75 http://static.flickr.com/206/476361508_a2e625415b_s.jpg
t for thumbnail, 100 on longest side
m for small, 240 on longest side
b for large, 1024 on longest side (only exists for very large original images)
If you omit the size prefix in the Flick URL, it will point to the medium sized image which has 500 pixels on the longest side.
Medium Size: http://static.flickr.com/206/476361508_a2e625415b.jpg
An important note - Flickr secures the original image with another secret code and it may not be possible to find the url of the Original size image without visiting the Flickr photo page.
The original image can have extensions like jpg, gif or png (depending on the source) but the resized flickr images alway have jpg as the extension.
Related: Flick Photo URLs have changed.