Are the equations in the Word file in proper Maple syntax, with asterisks used for multiplication and "less than or equal" represented as "<="?

I think that it is legitimate. Advanpix is using hardware quadruple precision (128-bit hardware floats). Maple doesn't have that. The quad precision is being compared against Maple's software floats with Digits set to 34.

@brian bovril Okay, here it is with the requested modification. Every time that it gets to a new longest sequence, it prints it and continues searching for the main sequence.

Note that for AD=210, n=11, the only possibilities are sequences starting with 11.

I did find the smallest example of AD = primorial(11), n=11, with the above code in under an hour. I think they were 7-digit  numbers.

IsPrime:= proc(n) option cache; isprime(n) end proc:

APSearch:= proc(AD::posint, n::posint)
     local SP:= 1, longest:= 0, j, k, S;
     do
          SP:= nextprime(SP);
          S:= SP + k*AD $ k = 1..n-1;
          if andmap(IsPrime, [S]) then
               return [SP, S]
          else
               for j from longest to n-1 do
                    if andmap(IsPrime, [S[1..j]]) then
                         longest:= j+1;
                         print([SP,S[1..j]])
                    else
                         break
                    end if
               end do
          end if           
     end do
end proc:   

APSearch(210,11);
                              [2]
                           [13, 223]
                         [13, 223, 433]
                      [13, 223, 433, 643]
                    [13, 223, 433, 643, 853]
                 [13, 223, 433, 643, 853, 1063]
              [47, 257, 467, 677, 887, 1097, 1307]
          [199, 409, 619, 829, 1039, 1249, 1459, 1669]
       [199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879]
    [199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089]
Warning,  computation interrupted

@brian bovril Okay, here it is with the requested modification. Every time that it gets to a new longest sequence, it prints it and continues searching for the main sequence.

Note that for AD=210, n=11, the only possibilities are sequences starting with 11.

I did find the smallest example of AD = primorial(11), n=11, with the above code in under an hour. I think they were 7-digit  numbers.

IsPrime:= proc(n) option cache; isprime(n) end proc:

APSearch:= proc(AD::posint, n::posint)
     local SP:= 1, longest:= 0, j, k, S;
     do
          SP:= nextprime(SP);
          S:= SP + k*AD $ k = 1..n-1;
          if andmap(IsPrime, [S]) then
               return [SP, S]
          else
               for j from longest to n-1 do
                    if andmap(IsPrime, [S[1..j]]) then
                         longest:= j+1;
                         print([SP,S[1..j]])
                    else
                         break
                    end if
               end do
          end if           
     end do
end proc:   

APSearch(210,11);
                              [2]
                           [13, 223]
                         [13, 223, 433]
                      [13, 223, 433, 643]
                    [13, 223, 433, 643, 853]
                 [13, 223, 433, 643, 853, 1063]
              [47, 257, 467, 677, 887, 1097, 1307]
          [199, 409, 619, 829, 1039, 1249, 1459, 1669]
       [199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879]
    [199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089]
Warning,  computation interrupted

alias(x= RootOf(_Z^3+_Z+1)):
Normal(1/x^2) mod 7;

alias(x= RootOf(_Z^3+_Z+1)):
Normal(1/x^2) mod 7;

Good point. But your `and` is superfluous and potentially dangerous (if you were dealing with <> inequalities it would evaluate). All the conditions in the expression sequence passed to solve (and most other commands) are assumed to be in conjunction.

Good point. But your `and` is superfluous and potentially dangerous (if you were dealing with <> inequalities it would evaluate). All the conditions in the expression sequence passed to solve (and most other commands) are assumed to be in conjunction.

@sunit If you can rearrange it to a first-order system, then you should do so. It looks straightforward to me also.

I was hoping that Preben would see this here. Give it a few days.

That's a really nice use of ``.

Maple gets the antiderivative to this almost instantly. So why does the definite integral take several seconds, even if I specify method= ftoc?

That's a really nice use of ``.

Maple gets the antiderivative to this almost instantly. So why does the definite integral take several seconds, even if I specify method= ftoc?

@sunit Even if I replace your a0 and d by 0, I still get an error "Unable to convert to a first-order system". I don't know why. Hopefully someone else will take a look at it. I think that Preben Alsholm could solve it. After that problem is solved, I think that the conditions with a0 and d can be easily handled with piecewise.

I think that you need one more initial condition. You don't have any for a[2].

You'll need to give an explicit example of an expression that gives the error.

@sunit I editted it for you.

@Art Kalb Ah, I think that I understand your problem: I think that you have the mistaken impression that the behaviour of f(g(x)) can be controlled by a procedure named `f/g` for arbitrary f and g. The reality is that that mechanism only works for a few select system routines f, for example, evalf, print, type, value, diff.