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Ingy döt Net 2026-02-01 16:33:20 -08:00
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Task/Cuban-primes/Ada/cuban-primes.ada
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-- Rosetta Code Task written in Ada
-- Cuban primes (related to "Cubes", not "Cubans")
-- https://rosettacode.org/wiki/Cuban_primes
-- July 2024, R. B. E.
-- Using this Cuban Primes Definition: primes of the form: n^3 - (n-1)^3.
-- ToDo:
-- Commatize the results (an advanced subtask)
-- Could replace the "activity dots" generated during the big calculations with a spinner
-- NOTE: Using GNAT Big_Numbers package.
-- Takes a very long time to generate the 100_000th cuban prime: about 75 minutes on a M1 Mac Mini.
pragma Ada_2022;
with Ada.Text_IO; use Ada.Text_IO;
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions;
with Ada.Numerics.Big_Numbers.Big_Integers; use Ada.Numerics.Big_Numbers.Big_Integers;
with Ada.Strings; use Ada.Strings;
with Ada.Strings.Fixed; use Ada.Strings.Fixed;
with Ada.Strings.Maps; use Ada.Strings.Maps;
with Ada.Real_Time; use Ada.Real_Time;
procedure Cuban_Primes is
function Is_Prime (A : Positive) return Boolean is
D : Positive;
begin
if A < 2 then
return False;
end if;
if A in 2 .. 3 then
return True;
end if;
if A mod 2 = 0 then
return False;
end if;
if A mod 3 = 0 then
return False;
end if;
D := 5;
while D * D <= A loop
if A mod D = 0 then
return False;
end if;
D := D + 2;
if A mod D = 0 then
return False;
end if;
D := D + 4;
end loop;
return True;
end Is_Prime;
function Is_Prime (A : Big_Natural) return Boolean is
D : Big_Natural;
B0 : constant Big_Natural := To_Big_Integer (0);
B1 : constant Big_Natural := To_Big_Integer (1);
B2 : constant Big_Natural := To_Big_Integer (2);
B3 : constant Big_Natural := To_Big_Integer (3);
B4 : constant Big_Natural := To_Big_Integer (4);
B5 : constant Big_Natural := To_Big_Integer (5);
begin
if A < B2 then
return False;
end if;
if (A = B2) or (A = B3) then
return True;
end if;
if A mod B2 = B0 then
return False;
end if;
if A mod B3 = B0 then
return False;
end if;
D := B5;
while D * D <= A loop
if A mod D = B0 then
return False;
end if;
D := D + B2;
if A mod D = B0 then
return False;
end if;
D := D + B4;
end loop;
return True;
end Is_Prime;
Cuban_Count : Natural := 1;
Candidate : Natural;
Big_Candidate : Big_Natural;
Max_Cuban_for_the_Table : constant Integer := 200;
Max_Cuban_below_the_Table : constant Integer := 100_000;
Start_Time, Stop_Time : Time;
Elapsed_Time : Time_Span;
begin
Put ("The first ");
Put (Max_Cuban_for_the_Table, 1);
Put_Line (" Cuban Primes...");
for I in 1 .. Integer'Last loop
Candidate := ((I + 1) ** 3) - (I ** 3);
if Is_Prime (Candidate) then
Put (Candidate, 8);
if ((Cuban_Count rem 14) = 0) then
New_Line;
end if;
Cuban_Count := Cuban_Count + 1;
end if;
exit when Cuban_Count > Max_Cuban_for_the_Table;
end loop;
New_Line (2);
Cuban_Count := 1;
Start_Time := Clock;
Put ("The ");
Put (Max_Cuban_below_the_Table, 1);
Put ("th Cuban Prime is: ");
for I in 1 .. Integer'Last loop
Big_Candidate := (((To_Big_Integer (I) + 1) ** 3) - (To_Big_Integer (I) ** 3));
if Is_Prime (Big_Candidate) then
Cuban_Count := Cuban_Count + 1;
if (Cuban_Count rem 10_000) = 0 then
Put (".");
end if;
end if;
exit when Cuban_Count = Max_Cuban_below_the_Table;
end loop;
New_Line;
Put (Trim (To_String (Big_Candidate), Right));
Stop_Time := Clock;
Elapsed_Time := Stop_Time - Start_Time;
New_Line;
Put_Line ("Elapsed time to calculate: " & Duration'Image (To_Duration (Elapsed_Time)) & " seconds");
end Cuban_Primes;