I'm no expert as I was brought up to believe that there are enough nukes to kill all humans 10 times over and you say there is only enough to kill 30% of humans. But, afaik, there will be no Internet after nukes - electromagnetic pulses all over the world will frazzle the routers.
I never ever said there are not
enough nukes (and Hydrogen bombs) to kill more than stated above, but the fact of the matter is:
1. Some people will keep themselves safe, for example if a "typical" atom bomb explodes half a mile from your house and you are inside a standard safe-room with 30 CM concrete walls, you won't be hit from the radiation until you leave the room.
2. The bombs will be aimed on specific locations, probably high population concentrations, but even so - the demographic of people includes many people living outside the dense areas.
3. There is a chance for some "safe havens" - maybe some countries won't be attacked at all.
4. Once it starts, there are large "safe rooms" the governments made for the population, and those get into those should be ok.
As for the EMP, that is a serious problem, mainly from an intentional emp bombs and not the side-effect caused by the nukes, even though a nuke can cause the emp, the effect is slim compared to an EMP directed to cause it in the right frequency and exploded in the right height.
Example for such a threat; North Korea launched a "Satellite" to orbit quite recently, and the USA threatened with sanctions if they will do so, they did not care about US threats and launched the Satellite. The US said that this should be looked at as a "long range missile experiment". Anyway, the point is, according to scientists, this Satellite, which was launched successfully btw, is not receiving or transmitting any data from or to earth... in other words they said it is not functioning as a satellite... There is some speculation as to "why would anyone launch a satellite which is not a satellite" into orbit.... and the main theory is that it is a weapon, capable of launching an emp over the US.
Now, why use an orbiting-device instead of launching a long-range missile if/when they wish to attack the US? simple; the oceans make the flight take time, and during this time the missile can be intercepted, now at the same time, it is also harder to launch such a missile because the launching movements will be seen and can be intercepted and also capabilities of launching a missile to such a long range (I.E NK to US) is hard to get.
So, a satalite, once it is above the US, can easily launch a missile that hits the sky of the us within seconds instead of minutes-of flight from UK to US.
Now, since the missile comes from above, there is a good chance it is an emp missile, as emp calculations show that the most effective way to dispatch the wave is by a balanced symmetric explosion in the sky above the area you want to hit.
much of the Internet's Infrastructure is under the sea and no one will waste bombs to go to the sea. However, power-surges will happen in many places since one of the "best" targets is the power supplies of different countries. Therefore power-surges can cause internet blackouts, but as Bitcoin is created and the way the Internet is created, once a country restores the power, the data moves on and it's like a "hit the hydra head" kind of game.
In fact, the internet was invented to allow the US preserve the information and survive a WWIII scenario, as the famous physic professor Michio Kaku stated in one of his lectures.
