Data update
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Ingy döt Net
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7735 changed files with 38060 additions and 199180 deletions
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-- Rosetta Code Task written in Ada
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-- Cuban primes (related to "Cubes", not "Cubans")
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-- https://rosettacode.org/wiki/Cuban_primes
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-- July 2024, R. B. E.
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-- Using this Cuban Primes Definition: primes of the form: n^3 - (n-1)^3.
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-- ToDo:
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-- Commatize the results (an advanced subtask)
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-- Could replace the "activity dots" generated during the big calculations with a spinner
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-- NOTE: Using GNAT Big_Numbers package.
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-- Takes a very long time to generate the 100_000th cuban prime: about 75 minutes on a M1 Mac Mini.
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pragma Ada_2022;
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with Ada.Text_IO; use Ada.Text_IO;
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with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
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with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions;
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with Ada.Numerics.Big_Numbers.Big_Integers; use Ada.Numerics.Big_Numbers.Big_Integers;
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with Ada.Strings; use Ada.Strings;
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with Ada.Strings.Fixed; use Ada.Strings.Fixed;
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with Ada.Strings.Maps; use Ada.Strings.Maps;
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with Ada.Real_Time; use Ada.Real_Time;
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procedure Cuban_Primes is
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function Is_Prime (A : Positive) return Boolean is
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D : Positive;
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begin
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if A < 2 then
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return False;
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end if;
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if A in 2 .. 3 then
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return True;
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end if;
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if A mod 2 = 0 then
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return False;
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end if;
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if A mod 3 = 0 then
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return False;
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end if;
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D := 5;
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while D * D <= A loop
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if A mod D = 0 then
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return False;
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end if;
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D := D + 2;
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if A mod D = 0 then
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return False;
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end if;
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D := D + 4;
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end loop;
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return True;
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end Is_Prime;
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function Is_Prime (A : Big_Natural) return Boolean is
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D : Big_Natural;
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B0 : constant Big_Natural := To_Big_Integer (0);
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B1 : constant Big_Natural := To_Big_Integer (1);
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B2 : constant Big_Natural := To_Big_Integer (2);
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B3 : constant Big_Natural := To_Big_Integer (3);
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B4 : constant Big_Natural := To_Big_Integer (4);
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B5 : constant Big_Natural := To_Big_Integer (5);
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begin
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if A < B2 then
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return False;
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end if;
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if (A = B2) or (A = B3) then
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return True;
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end if;
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if A mod B2 = B0 then
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return False;
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end if;
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if A mod B3 = B0 then
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return False;
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end if;
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D := B5;
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while D * D <= A loop
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if A mod D = B0 then
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return False;
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end if;
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D := D + B2;
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if A mod D = B0 then
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return False;
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end if;
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D := D + B4;
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end loop;
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return True;
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end Is_Prime;
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Cuban_Count : Natural := 1;
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Candidate : Natural;
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Big_Candidate : Big_Natural;
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Max_Cuban_for_the_Table : constant Integer := 200;
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Max_Cuban_below_the_Table : constant Integer := 100_000;
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Start_Time, Stop_Time : Time;
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Elapsed_Time : Time_Span;
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begin
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Put ("The first ");
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Put (Max_Cuban_for_the_Table, 1);
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Put_Line (" Cuban Primes...");
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for I in 1 .. Integer'Last loop
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Candidate := ((I + 1) ** 3) - (I ** 3);
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if Is_Prime (Candidate) then
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Put (Candidate, 8);
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if ((Cuban_Count rem 14) = 0) then
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New_Line;
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end if;
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Cuban_Count := Cuban_Count + 1;
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end if;
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exit when Cuban_Count > Max_Cuban_for_the_Table;
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end loop;
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New_Line (2);
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Cuban_Count := 1;
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Start_Time := Clock;
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Put ("The ");
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Put (Max_Cuban_below_the_Table, 1);
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Put ("th Cuban Prime is: ");
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for I in 1 .. Integer'Last loop
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Big_Candidate := (((To_Big_Integer (I) + 1) ** 3) - (To_Big_Integer (I) ** 3));
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if Is_Prime (Big_Candidate) then
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Cuban_Count := Cuban_Count + 1;
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if (Cuban_Count rem 10_000) = 0 then
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Put (".");
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end if;
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end if;
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exit when Cuban_Count = Max_Cuban_below_the_Table;
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end loop;
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New_Line;
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Put (Trim (To_String (Big_Candidate), Right));
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Stop_Time := Clock;
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Elapsed_Time := Stop_Time - Start_Time;
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New_Line;
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Put_Line ("Elapsed time to calculate: " & Duration'Image (To_Duration (Elapsed_Time)) & " seconds");
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end Cuban_Primes;
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@ -1,34 +1,32 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">np</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">p3</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">*</span><span style="color: #000000;">1</span><span style="color: #0000FF;">*</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">i3</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
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<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
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<span style="color: #000000;">pn</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
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with javascript_semantics
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include mpfr.e
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integer np = 0,
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i = 2
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mpz p3 = mpz_init(1*1*1),
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i3 = mpz_init(),
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p = mpz_init(),
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pn = mpz_init()
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"The first 200 cuban primes are:\n"</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">first200</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()=</span><span style="color: #004600;">JS</span><span style="color: #0000FF;">?</span><span style="color: #000000;">10000</span><span style="color: #0000FF;">:</span><span style="color: #000000;">100000</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">while</span> <span style="color: #000000;">np</span><span style="color: #0000FF;"><</span><span style="color: #000000;">lim</span> <span style="color: #008080;">do</span>
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<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpz_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
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<span style="color: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">np</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">np</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">200</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">first200</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">first200</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%,9d"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_get_integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pn</span><span style="color: #0000FF;">)))</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">np</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">first200</span><span style="color: #0000FF;">[-</span><span style="color: #000000;">10</span><span style="color: #0000FF;">..-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]))</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i3</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nThe %,dth cuban prime is %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">np</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">comma_fill</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)})</span>
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<span style="color: #0000FF;">{</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_free</span><span style="color: #0000FF;">({</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">})</span>
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<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>
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<!--
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printf(1,"The first 200 cuban primes are:\n")
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sequence first200 = {}
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atom t0 = time()
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constant lim = iff(platform()=JS?10000:100000)
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while np<lim do
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mpz_ui_pow_ui(i3,i,3)
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mpz_sub(p,i3,p3)
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if mpz_prime(p) then
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mpz_set(pn,p)
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np += 1
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if np<=200 then
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first200 = append(first200,sprintf("%,9d",mpz_get_integer(pn)))
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if mod(np,10)=0 then
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printf(1,"%s\n",join(first200[-10..-1]))
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end if
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end if
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end if
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mpz_set(p3,i3)
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i += 1
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end while
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printf(1,"\nThe %,dth cuban prime is %s\n",{np,mpz_get_str(pn,comma_fill:=true)})
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{p3,i3,p} = mpz_free({p3,i3,p})
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?elapsed(time()-t0)
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@ -1,5 +1,5 @@
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-- 28 Jul 2025
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include Settings
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-- 23 Aug 2025
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include Setting
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numeric digits 20
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say 'CUBAN PRIMES'
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