Help:=proc(): print(`SA(n), IsDiv(n,L), OneStep(L)`) :
print(`PrimeList(N), PrimeListM(N) `):
end :


#SA(n): The list of primes <= n
SA:=proc(n) local i,j:
{seq(i,i=1..n)} minus 
{seq(seq(j*i,i=2..n/j),j=2..trunc(sqrt(n)))} minus {1}:

end:


#IsDiv(n,L): inputs a pos. integer n and a list
#of pos. integers L, and outputs true if
#n is divisible by any of the members of L

IsDiv:=proc(n,L) local i:
for i from 1 to nops(L) do 
 if n mod L[i]=0 then
  RETURN(true):
 fi:
od:
false:

end:


#OneStep(L): inputs the list of the first primes
#and outputs the same list with one more prime that
#comes right after
OneStep:=proc(L) local i,n:
#n is the largest prime so-far
n:=L[nops(L)]:

 for i from n+1 while IsDiv(i,L) do od:

[op(L),i]:

end:

#The list of the first N prime numbers, our way
PrimeList:=proc(N) local i,L:
L:=[2]:
for i from 2 to N do
 L:=OneStep(L):
od:
L:
end:

#The list of the first N prime numbers, the Maple way
PrimeListM:=proc(N) local i:
 [seq(ithprime(i),i=1..N)]:
end: