Problem Statement

The Euclid–Mullin sequence is an infinite sequence of distinct prime numbers, in which each element is the least prime factor of one plus the product of all earlier elements. The first element is usually assumed to be 2. So the second element is : (2) + 1 = 3 and the third element is : (2 x 3) + 1 = 7 as this is prime. Although intermingled with smaller elements, the sequence can produce very large elements quite quickly and only the first 51 have been computed at the time of writing. Compute and show here the first 16 elements of the sequence or, if your language does not support arbitrary precision arithmetic, as many as you can. Compute the next 11 elements of the sequence. OEIS sequence A000945

Let's start with the solution:

Func Firstfac(n) = 
    j := 3;
    up := Sqrt(n);
    
    while j <= up do
        if Divides(j,n) then Return(j) fi;
        j:=j+2;
    od;
    Return(n).;
    
Array eu[16];
eu[1]:=2;
!(eu[1],' ');
for i=2 to 16 do
    eu[i]:=Firstfac(1+Prod[eu[k]]);
    !(eu[i],' ');
od;