If you're wondering whether you need a Core i5 processor or whether you should I buy a dual-core or quad-core CPU, here's some help so you can make a decision.
When we say 'undemanding' we mean just about everything bar gaming and video editing. 3D rendering and other intensive applications are also excluded from the undemanding list. Essentially, if you just want to do all the normal things people do with their computers - email, web browsing, YouTube, editing and sharing photos, Microsoft Office - a basic processor is fine.
PC processors: How many cores do I need?
You rarely, if ever, see single-core processors any more, and it's well worth avoiding these in laptops and PCs. More cores generally means more performance, but more importantly, the ability to run multiple applications at the same time.
Some applications can also take advantage of multiple cores so even if you're only running that one program, you'll see an improvement in its performance. Strictly speaking, though, there's never just one program running, since Windows itself uses processing power, and CPU time has to be divided up between the operating system and any programs you're running.
The law of diminishing returns applies, so the latest octacore or even dodeca-core isn't going to mean 8x or 12x better performance.
Bottom line: you need at least two cores, but four is better.
PC processors: Do I need a Core i3, i5 or i7?
This is a similar, but subtly different question from 'how many cores'. Generally, you get what you pay for, so more expensive processors are faster. But how fast do you need?
These days you can't just go by clock speed. You have to take into account the number of cores, the cache and the speed in GHz.
Even then it's tricky, as there are other factors, such as the process used and the amount of power a processor uses.
Newer processors are generally always more power efficient, which is important in laptops. You either get more battery life for the same performance, or more performance for the same battery life.
To answer the question, though, you don't need a Core processor for those undemanding tasks we mentioned above. A Pentium or even Celeron will do the job. But depending on the exact processor, you might find everything a little slow and unresponsive. It's best to check reviews of that individual processor, or reviews of the particular laptop or PC you're considering buying before making any decisions.