For all those of you who are having trouble finding Deep Core Asteroids to blow up, try going to some Belt Clusters:
This was not a one-off, either - while in Benebdjetet, I visited five Belt Clusters, and three of them contained a Deep Core Asteroid (two of Rhodplumsite, and one of Painite). I haven't tried this anywhere else, so I don't know how common it is in other star systems... but Benebdjetet's Belt Clusters are nothing special (Metal Rich, Major Reserves), so I assume you will be able to find them in Belt Clusters all over the place!
Incidentally, once you blow up an asteroid, it stays blown up for a certain period of time - and I detonated those three asteroids last night, so if you go to Benebdjetet right now, they might not have re-spawned yet. (Are they persistent for different players? Again, I assume so...)
I did go back to see if I could 'farm' the asteroid, and when I first jumped back into the Belt Cluster, there was no sign of it, detonated or otherwise. But then, while I was fighting the pirate, I noticed an asteroid 'pop-in' in the distance - and then a fraction of a second later it 'remembered' that I had already destroyed it, and it transformed into its fractured state, complete with dust cloud. So if, upon arriving in a Belt Cluster, you ping your Pulse Wave Scanner and don't see anything, be patient - the Deep Core Asteroid might not appear for a few seconds, or it might only appear when you get close, I'm not sure.
But they can be found in Belt Clusters, so take a look!

This was not a one-off, either - while in Benebdjetet, I visited five Belt Clusters, and three of them contained a Deep Core Asteroid (two of Rhodplumsite, and one of Painite). I haven't tried this anywhere else, so I don't know how common it is in other star systems... but Benebdjetet's Belt Clusters are nothing special (Metal Rich, Major Reserves), so I assume you will be able to find them in Belt Clusters all over the place!
Incidentally, once you blow up an asteroid, it stays blown up for a certain period of time - and I detonated those three asteroids last night, so if you go to Benebdjetet right now, they might not have re-spawned yet. (Are they persistent for different players? Again, I assume so...)
I did go back to see if I could 'farm' the asteroid, and when I first jumped back into the Belt Cluster, there was no sign of it, detonated or otherwise. But then, while I was fighting the pirate, I noticed an asteroid 'pop-in' in the distance - and then a fraction of a second later it 'remembered' that I had already destroyed it, and it transformed into its fractured state, complete with dust cloud. So if, upon arriving in a Belt Cluster, you ping your Pulse Wave Scanner and don't see anything, be patient - the Deep Core Asteroid might not appear for a few seconds, or it might only appear when you get close, I'm not sure.
But they can be found in Belt Clusters, so take a look!