Q:

Electric Range Keeps Blowing its Fuse

I have a brand new electric range that I am having a problem with and would appreciate some insights so that I can determine whether its the appliance or my electricity is at fault.
When I turn on 2 or more burners on the stove-top or 1 burner and the oven, I can feel the plug getting extremely hot and the range will just shut off after some time. After opening the plug, I see the fuse is blown. I replaced the fuse and the same thing happened again. When having only 1 burner on then everything is fine.
I've done lots of reading but I am still unable to understand why is this happening.
The range's plug is rated 250V and fitted with a 13A fuse. It is plugged into a wall socket. I have checked the main circuit breaker (100 AMP MAX - 30 AMP for each switch), when turning off one specific switch only the wall socket used by my range is turned off, so no other appliances are loaded on the same circuit.
With that said, what could be causing this? Is it my circuit not having sufficient power for the range? But if this was the issue then, according to stuff I read, the circuit breaker switch should trip not the plug's fuse get blown.
When opening the plug, I see the wire going to the right side pin fried but others are fine.

Appreciate if someone can provide some info.
EDIT:
Thanks to gbulmer now I see it is wired incorrectly! I will rewire it correctly but I have a side question. Could the incorrect wiring done damage to the appliance or not?

A:

As gbulmer pointed out, the plug is wired incorrectly.
That plug is damaged, I would replace it.
Trim back any damaged wire (with burnt insulation) and make sure the earth wire has the most slack (so it is disconnected last if the cable is pulled out of the plug).
A typical electric hob ring can need 1.7 kW. Two of those would overload a 13A circuit.
I would check the rating of the electric range. High current appliances of that sort are normally connected directly to a dedicated 20A or 32A circuit using a switched wiring box, not plugged into a normal ring-main using a normal 13A plug. If the 13A fuse is overheating or blowing it suggests the range is overloading the socket. I would consult an electrician.

In my home, I have a 32A circuit that feeds the separate electric oven and electric hob (4 rings) - each is connected through a switch as shown above (one labelled "hob", the other "oven"). Your "range" probably needs a dedicated circuit and isolating switch.

