They do have a relatively decent amount of hydrolectric generation capacity. But using some of that for bitcoin mining would depend on whether or not they generate electricity in excess of demand. I doubt there is much generation capacity remaining beyond demand (which I gathered, glancing at the following), but maybe the actual data would show that is possible.
Central African Republic - Energy Consumption and Production
But even if they did have plenty of excess generation capacity that was from renewables (e.g., hydroelectric, or wind) otherwise going unused, a bitcoin mining operation requires an incredible amount of CapEx, and it is not all that likely a mining op would locate in a country that is currently in a civil war. They had to bring in a Russian security group to protect their diamond mines. A potentially hostile environment is not going to be attractive no matter what the cost per kWh is.
Now it is entirely possible there could be pockets of opportunity. Especially if there is commoditization of ASIC hardware, making it economical that mining can be done with PV (solar) generation, even when the equipment would not be operating more than the eight or whatever hours of the day where there is sufficient sunlight.
But as far as industrial bitcoin mining ops, the Central African Republic is not likely to see any of that at this point in time.
But here's an example of on of those "pockets of opportunity".
Here's a problem needing an effective and affordable solution: Drying of grains in rural areas
The CapEx (equipment) and OpEx (electricity or flame) for drying of grains and other agricultural products is so high that the ultra-low cost alternative is to simply spread the grains on the shoulder of a tarmacked road and let the sun do its magic. Yummy, right? And just pray that nobody gets run over.
Of course, bitcoin mining rigs produce heat that is suitable for grain drying. So even if the cost per kWh is higher such that mining is essentially a wash (little no profit from mining), that might still be done so as to use the ventilated heat be used for drying grains. There are commercial grain dryers, many of which run on natural gas, and some that use electricity for heat, but I'm not aware of any that have been fabricated to use heat coming from bitcoin ASIC mining rigs. Bitcoin mining very well could be useful for this.
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