Prime numbers have held a fascination for mathematicians for centuries. It is stimulating and beneficial for those in the early stages of developing their maths skills to spend some time thinking about them. A great deal of time ~ in early years ~ is spent in learning times tables ~ the products of two simple numbers. That, by definition, excludes learning much about the prime numbers. I am not suggesting that as much attention should be given to primes.
From my experience insufficient attention is paid ~ when learning tables ~ to the factors of simple numbers ~ those under 100. This is a fancy way of saying that pupils spend too little time on the backwards learning of multiplication tables. For example 'Tell me two numbers which multiply together to make 72' is more thought provoking than 'What is eight time nine?' For one thing there are several answers. For someone who really knows their tables well 72 is the familiar product of 9×8, or maybe the slightly less familiar 8×9. Those born prior to he 1940s will probably think of 6×12. (I believe the eleven and twelve times tables are required learning on some syllabuses.) Strangely enough I immediately thought of 2x36. I wonder whether that is a symptom of being naively-minded?
You will have to do a fair bit of trial and error to work out prime numbers if you are not familiar with them. For example ~ Is 17 a prime number? Try 2x8=16, 2x9=18...it is not divisible by 2. Next try ~ 3x5=15 ~ 3x6=18 ~ nor 3. Next try 5x3=15 ~ 5x4=20. ~ Next try 7x2=14 ~ 7x3=21. Next is 11...and that does not work either.So 17 is a prime number. All this is much easier if you know your times-tables well