"Taking a list of numeric values L, and producing a list of lists [p,f(p)] for every p in L , is not complicated. In fact it is a quite straightforward and rather basic example of Maple programming"

This sentence i don't understand yet, so i must see a example?

On my maple page i got also all the time typesetting info ?
Looked at the help page :NumberTheory,PrimeCounting

How to produce the graph of the prime counting function with the two approximations?

When should i use ->  for a procedure definition and when not ?
In my post i do see examples of  procedures which are made on two different ways.
proc  ..end proc;

Still difficult to get a procedure on two ways 

test:=x->x^2;
Typesetting:-mprintslash([(test := x -> x^2)],[x -> x^2])

test(2);
4

restart;
test:= proc()
local x,a;
a:= x^2;
end ;
Typesetting:-mprintslash([(test := proc () local x, a; a := x^2; end proc)],[
proc () local x, a; a := x^2; end proc])

test(2);
x^2

test(3);
x^2

As you can see with the standard proc definition i getlost with  calculating x^2 

Can i make a natural numberline what shows the enumber of primes at each of 1000 numbers  
I have her

0-1000 : 168
1000 -2000: 135

2000-3000 : 127

3000- 4000: 120

4000 -5000 : 119 

then a gap (jump) 

10^7- 1000- 10^7  : 53 

You can see that the "number of primes"  is fluctuating
Can i make a procedure what calculates the latest mersenne prime number ?
Problem is only that there is a theorem: there are arbitrary long series of divisible numbers on the numberline 
There are gaps of length n - 1, where are no primenumbers  in positioned.

The idea is to get a idea of the distribution of primes to make a guess from where to start to find another one? 

In the obselote book programming examples it is using array's as data type

Is het easier to use A Vector or Matrix as datatype?