Data update
This commit is contained in:
Ingy döt Net
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7735 changed files with 38060 additions and 199180 deletions
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@ -1,58 +0,0 @@
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with Ada.Text_Io;
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procedure Additive_Primes is
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Last : constant := 499;
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Columns : constant := 12;
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type Prime_List is array (2 .. Last) of Boolean;
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function Get_Primes return Prime_List is
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Prime : Prime_List := (others => True);
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begin
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for P in Prime'Range loop
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if Prime (P) then
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for N in 2 .. Positive'Last loop
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exit when N * P not in Prime'Range;
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Prime (N * P) := False;
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end loop;
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end if;
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end loop;
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return Prime;
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end Get_Primes;
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function Sum_Of (N : Natural) return Natural is
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Image : constant String := Natural'Image (N);
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Sum : Natural := 0;
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begin
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for Char of Image loop
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Sum := Sum + (if Char in '0' .. '9'
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then Natural'Value ("" & Char)
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else 0);
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end loop;
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return Sum;
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end Sum_Of;
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package Natural_Io is new Ada.Text_Io.Integer_Io (Natural);
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use Ada.Text_Io, Natural_Io;
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Prime : constant Prime_List := Get_Primes;
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Count : Natural := 0;
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begin
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Put_Line ("Additive primes <500:");
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for N in Prime'Range loop
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if Prime (N) and then Prime (Sum_Of (N)) then
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Count := Count + 1;
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Put (N, Width => 5);
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if Count mod Columns = 0 then
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New_Line;
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end if;
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end if;
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end loop;
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New_Line;
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Put ("There are ");
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Put (Count, Width => 2);
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Put (" additive primes.");
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New_Line;
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end Additive_Primes;
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@ -1,73 +0,0 @@
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IDENTIFICATION DIVISION.
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PROGRAM-ID. ADDITIVE-PRIMES.
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DATA DIVISION.
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WORKING-STORAGE SECTION.
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01 VARIABLES.
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03 MAXIMUM PIC 999.
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03 AMOUNT PIC 999.
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03 CANDIDATE PIC 999.
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03 DIGIT PIC 9 OCCURS 3 TIMES,
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REDEFINES CANDIDATE.
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03 DIGITSUM PIC 99.
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01 PRIME-DATA.
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03 COMPOSITE-FLAG PIC X OCCURS 500 TIMES.
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88 PRIME VALUE ' '.
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03 SIEVE-PRIME PIC 999.
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03 SIEVE-COMP-START PIC 999.
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03 SIEVE-COMP PIC 999.
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03 SIEVE-MAX PIC 999.
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01 OUT-FMT.
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03 NUM-FMT PIC ZZZ9.
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03 OUT-LINE PIC X(40).
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03 OUT-PTR PIC 99.
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PROCEDURE DIVISION.
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BEGIN.
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MOVE 500 TO MAXIMUM.
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MOVE 1 TO OUT-PTR.
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PERFORM SIEVE.
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MOVE ZERO TO AMOUNT.
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PERFORM TEST-NUMBER
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VARYING CANDIDATE FROM 2 BY 1
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UNTIL CANDIDATE IS GREATER THAN MAXIMUM.
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DISPLAY OUT-LINE.
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DISPLAY SPACES.
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MOVE AMOUNT TO NUM-FMT.
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DISPLAY 'Amount of additive primes found: ' NUM-FMT.
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STOP RUN.
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TEST-NUMBER.
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ADD DIGIT(1), DIGIT(2), DIGIT(3) GIVING DIGITSUM.
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IF PRIME(CANDIDATE) AND PRIME(DIGITSUM),
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ADD 1 TO AMOUNT,
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PERFORM WRITE-NUMBER.
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WRITE-NUMBER.
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MOVE CANDIDATE TO NUM-FMT.
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STRING NUM-FMT DELIMITED BY SIZE INTO OUT-LINE
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WITH POINTER OUT-PTR.
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IF OUT-PTR IS GREATER THAN 40,
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DISPLAY OUT-LINE,
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MOVE SPACES TO OUT-LINE,
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MOVE 1 TO OUT-PTR.
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SIEVE.
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MOVE SPACES TO PRIME-DATA.
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DIVIDE MAXIMUM BY 2 GIVING SIEVE-MAX.
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PERFORM SIEVE-OUTER-LOOP
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VARYING SIEVE-PRIME FROM 2 BY 1
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UNTIL SIEVE-PRIME IS GREATER THAN SIEVE-MAX.
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SIEVE-OUTER-LOOP.
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IF PRIME(SIEVE-PRIME),
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MULTIPLY SIEVE-PRIME BY 2 GIVING SIEVE-COMP-START,
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PERFORM SIEVE-INNER-LOOP
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VARYING SIEVE-COMP
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FROM SIEVE-COMP-START BY SIEVE-PRIME
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UNTIL SIEVE-COMP IS GREATER THAN MAXIMUM.
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SIEVE-INNER-LOOP.
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MOVE 'X' TO COMPOSITE-FLAG(SIEVE-COMP).
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@ -28,11 +28,11 @@ var T: integer;
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begin
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Result:=0;
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repeat
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begin
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T:=N mod 10;
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N:=N div 10;
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Result:=Result+T;
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end
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begin
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T:=N mod 10;
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N:=N div 10;
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Result:=Result+T;
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end
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until N<1;
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end;
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@ -48,15 +48,15 @@ Cnt:=0;
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S:='';
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for N:=1 to 500-1 do
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if IsPrime(N) then
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begin
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Sum:=SumDigits(N);
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if IsPrime(Sum) then
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begin
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Inc(Cnt);
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S:=S+Format('%6d',[N]);
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if (Cnt mod 8)=0 then S:=S+CRLF;
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end;
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end;
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begin
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Sum:=SumDigits(N);
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if IsPrime(Sum) then
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begin
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Inc(Cnt);
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S:=S+Format('%6d',[N]);
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if (Cnt mod 8)=0 then S:=S+CRLF;
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end;
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end;
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Memo.Lines.Add(S);
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Memo.Lines.Add('Count = '+IntToStr(Cnt));
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end;
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@ -2,35 +2,35 @@
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# Prime numbers for which the sum of their decimal digits are also primes
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# # Variables:
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# # Variables:
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#
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integer MAX_n=500
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# # Functions:
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# # Functions:
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#
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# # Function _isprime(n) return 1 for prime, 0 for not prime
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# # Function _isprime(n) return 1 for prime, 0 for not prime
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#
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function _isprime {
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typeset _n ; integer _n=$1
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typeset _i ; integer _i
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typeset _n ; integer _n=$1
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typeset _i ; integer _i
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(( _n < 2 )) && return 0
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for (( _i=2 ; _i*_i<=_n ; _i++ )); do
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(( ! ( _n % _i ) )) && return 0
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done
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return 1
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(( _n < 2 )) && return 0
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for (( _i=2 ; _i*_i<=_n ; _i++ )); do
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(( ! ( _n % _i ) )) && return 0
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done
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return 1
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}
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# # Function _sumdigits(n) return sum of n's digits
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# # Function _sumdigits(n) return sum of n's digits
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#
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function _sumdigits {
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typeset _n ; _n=$1
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typeset _i _sum ; integer _i _sum=0
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typeset _n ; _n=$1
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typeset _i _sum ; integer _i _sum=0
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for ((_i=0; _i<${#_n}; _i++)); do
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(( _sum+=${_n:${_i}:1} ))
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done
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echo ${_sum}
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for ((_i=0; _i<${#_n}; _i++)); do
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(( _sum+=${_n:${_i}:1} ))
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done
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echo ${_sum}
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}
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######
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@ -39,9 +39,9 @@ function _sumdigits {
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integer i digsum
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for ((i=2; i<MAX_n; i++)); do
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_isprime ${i} && (( ! $? )) && continue
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_isprime ${i} && (( ! $? )) && continue
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digsum=$(_sumdigits ${i})
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_isprime ${digsum} ; (( $? )) && printf "%4d " ${i}
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digsum=$(_sumdigits ${i})
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_isprime ${digsum} ; (( $? )) && printf "%4d " ${i}
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done
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print
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@ -1,6 +1,6 @@
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val isPrime = fn(i) {
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i == 2 or i > 2 and
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not any(series(2 .. i ^/ 2, asconly=true), by=fn x:i div x)
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i == 2 or i > 2 and
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not any(series(2 .. i ^/ 2, asconly=true), by=fn x:i div x)
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}
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val sumDigits = fn i: fold(s2n(string(i)), by=fn{+})
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@ -1,28 +1,28 @@
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isPrime = function(n)
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if n <= 3 then return n > 1
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if n % 2 == 0 or n % 3 == 0 then return false
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i = 5
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while i ^ 2 <= n
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if n % i == 0 or n % (i + 2) == 0 then return false
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i += 6
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end while
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return true
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if n <= 3 then return n > 1
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if n % 2 == 0 or n % 3 == 0 then return false
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i = 5
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while i ^ 2 <= n
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if n % i == 0 or n % (i + 2) == 0 then return false
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i += 6
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end while
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return true
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end function
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digitSum = function(n)
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sum = 0
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while n > 0
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sum += n % 10
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n = floor(n / 10)
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end while
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return sum
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sum = 0
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while n > 0
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sum += n % 10
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n = floor(n / 10)
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end while
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return sum
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end function
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additive = []
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for i in range(2, 500)
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if isPrime(i) and isPrime(digitSum(i)) then additive.push(i)
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if isPrime(i) and isPrime(digitSum(i)) then additive.push(i)
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end for
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print "There are " + additive.len + " additive primes under 500."
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print additive
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@ -1,7 +1,7 @@
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MODULE AdditivePrimes;
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IMPORT
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Out;
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Out, Primes;
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CONST
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Max = 500;
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@ -20,24 +20,8 @@ PROCEDURE DigitSum( n :INTEGER ):INTEGER;
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RETURN result
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END DigitSum;
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PROCEDURE Sieve;
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VAR i, j :INTEGER;
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BEGIN
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Prime[ 0 ] := FALSE; Prime[ 1 ] := FALSE;
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FOR i := 2 TO Max DO Prime[ i ] := TRUE END;
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FOR i := 2 TO Max DIV 2 DO
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IF Prime[ i ] THEN
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j := i * 2;
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WHILE j <= Max DO
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Prime[ j ] := FALSE;
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INC( j, i )
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END
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END
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END
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END Sieve;
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BEGIN
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Sieve;
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Primes.sieve( Prime );
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FOR n := 2 TO Max DO
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IF Prime[ n ] & Prime[ DigitSum( n ) ] THEN
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Out.Int( n, 4 );
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@ -1,6 +1,4 @@
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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;">function</span> <span style="color: #000000;">additive</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">)))</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">filter</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">get_primes_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">500</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">),</span><span style="color: #000000;">additive</span><span style="color: #0000FF;">)</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;">"%d additive primes found: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">))})</span>
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<!--
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with javascript_semantics
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function additive(string p) return is_prime(sum(sq_sub(p,'0'))) end function
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sequence res = filter(apply(get_primes_le(500),sprint),additive)
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printf(1,"%d additive primes found: %s\n",{length(res),join(shorten(res,"",6))})
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@ -1,5 +1,5 @@
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-- 22 Mar 2025
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include Settings
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-- 23 Aug 2025
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include Setting
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say 'ADDITIVE PRIMES'
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say version
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@ -22,7 +22,4 @@ say a 'additive primes found below' n
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say Time('e')/1 'seconds'
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exit
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include Sequences
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include Numbers
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include Functions
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include Abend
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include Math
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