Firstly it seems that the 'heavy' bases are more likely to produce an octo than the 'light' bases. So n=52, 67, 70, 82, 97, 112, 115, 142, ... (bases with weight >= 40) would be a good place to start searching. With this reasoning (whether sound or not) I discovered:

65498827395 67

...

In an attempt to make this search a bit more organised I've created a text file listing what has already been searched. I'll try to update this regularly, and as often as possible.

Btw, tell me if I've missed anything or you've searched a region more than what is listed.

In this file, a typical base would look like this:

<k> <n> <discoverer>

<k> <n> <discoverer>

...

<k> <n> <discoverer> (searched/2^n)

if an octo exists, and

<n> (searched/2^n)

otherwise. This way we can hopefully not redo others work.

PS: If I haven't missed any, we now know of 97 octoproth-primes. Hopefully we'll make the 100 mark soon.

PS2: Most wanted octoproths-primes: base 32, 63.