Data update
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Ingy döt Net
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1853 changed files with 35514 additions and 9441 deletions
89
Task/Blum-integer/Ada/blum-integer.ada
Normal file
89
Task/Blum-integer/Ada/blum-integer.ada
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@ -0,0 +1,89 @@
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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.Float_Text_IO; use Ada.Float_Text_IO;
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procedure Blum is
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Inc : Constant array (1 .. 8) of Integer := (4, 2, 4, 2, 4, 6, 2, 6);
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function Is_Prime (N : Integer) return Boolean is
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D : Integer := 5;
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begin
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if N < 2 then return False; end if;
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if N mod 2 = 0 then return N = 2; end if;
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if N mod 3 = 0 then return N = 3; end if;
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while D * D <= N loop
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if N mod D = 0 then return False; end if;
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D := D + 2;
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if N mod D = 0 then return False; 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 First_Prime_Factor (N : Integer) return Integer is
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D : Integer := 7;
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I : Integer := 1;
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begin
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if N = 1 then return 1; end if;
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if N mod 3 = 0 then return 3; end if;
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if N mod 5 = 0 then return 5; end if;
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while D * D <= N loop
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if N mod D = 0 then
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return D;
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end if;
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D := D + Inc(I);
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I := (I mod 8) + 1;
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end loop;
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return N;
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end First_Prime_Factor;
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I, Blum_Count : Integer := 1;
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J, P, Q : Integer;
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Blums : Array (1 .. 50) of Integer;
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Counts : Array (1 .. 4) of Integer := (others => 0);
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Final_Digits : Array (1 .. 4) of Integer := (1, 3, 7, 9);
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begin
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loop
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P := First_Prime_Factor(I);
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if P mod 4 = 3 then
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Q := I / P;
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if Q /= P and Q mod 4 = 3 and Is_Prime(Q) then
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if Blum_Count < 51 then Blums(Blum_Count) := I; end if;
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Counts(((I mod 10) / 3) + 1) := Counts(((I mod 10) / 3) + 1) + 1;
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Blum_Count := Blum_Count + 1;
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if Blum_Count = 51 then
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Put("First 50 Blum Integers:"); New_Line;
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for J in Integer range 1 .. 50 loop
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Put(Item => Blums(J), Width => 3); Put(" ");
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if J mod 10 = 0 then New_Line; end if;
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end loop;
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New_Line;
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elsif Blum_Count = 26829 or Blum_Count mod 100000 = 1 then
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Put("The "); Put(Item => Blum_Count, Width => 7);
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Put("th Blum Integer is: "); Put(Item => I, Width => 9);
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New_Line;
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if Blum_Count = 400001 then
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New_Line; Put("% Distribution of the First 400,000 Blum Integers:"); New_Line;
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for J in Integer range 1 .. 4 loop
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Put(" "); Put(Item => Float(Counts(J)) / 4000.0, Fore => 2, Aft => 3, Exp => 0);
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Put("% end in "); Put(Item => Final_Digits(J), Width => 1);
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New_Line;
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end loop;
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exit;
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end if;
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end if;
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end if;
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end if;
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if I mod 5 = 3 then
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I := I + 4;
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else
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I := I + 2;
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end if;
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end loop;
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end Blum;
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158
Task/Blum-integer/Fortran/blum-integer.f
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158
Task/Blum-integer/Fortran/blum-integer.f
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@ -0,0 +1,158 @@
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program BlumInteger
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use, intrinsic :: iso_fortran_env, only: int32, int64
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implicit none
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integer(int32), parameter :: LIMIT = 10*1000*1000
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integer(int32), allocatable :: BlumPrimes(:)
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integer(int32), allocatable :: BlumPrimes2(:)
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logical :: BlumField(0:LIMIT)
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integer(int32) :: EndDigit(0:9)
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integer(int64) :: k
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integer(int32) :: n, idx, j, P4n3Cnt,xx,yy
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call system_clock(count=xx)
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call Sieve4n_3_Primes(LIMIT, BlumPrimes2)
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! allocate(blumprimes(0:size(BlumPrimes2)-1))
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! The blumprimes2 array is allocated in the subroutine as a zero based array
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! but, the main program doesn't know that and assumes it's 1 based so we allocate
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! a zero based array then use move_alloc to correctly resize it a transfer the data
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allocate(blumprimes(0:1))
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call move_alloc(blumprimes2,blumprimes)
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P4n3Cnt = size(BlumPrimes) -1
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print *, 'There are ', CommaUint(int(P4n3Cnt, int64)), ' needed primes 4*n+3 to Limit ', CommaUint(int(LIMIT, int64))
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P4n3Cnt = P4n3Cnt - 1
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print *
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! Generate Blum-Integers
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BlumField = .false.
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do idx = 0, P4n3Cnt
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n = BlumPrimes(idx)
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do j = idx+1, P4n3Cnt
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k = int(n, int64) * int(BlumPrimes(j), int64)
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if (k > LIMIT) exit
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BlumField(k) = .true.
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end do
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end do
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call system_clock(count=yy)
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print *, 'First 50 Blum-Integers '
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idx = 0
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j = 0
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do
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do while (idx < LIMIT .and. .not. BlumField(idx))
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idx = idx + 1
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end do
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if (idx == LIMIT) exit
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if (mod(j, 10) == 0 .and. j /= 0) print *
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write(*, '(I5)', advance='no') idx
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j = j + 1
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idx = idx + 1
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if (j >= 50) exit
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end do
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print '(//)'
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print *, ' relative occurence of digit'
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print *, ' n.th |BlumInteger|Digit: 1 3 7 9'
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idx = 0
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j = 0
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n = 0
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k = 26828
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EndDigit = 0
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do
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do while (idx < LIMIT .and. .not. BlumField(idx))
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idx = idx + 1
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end do
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if (idx == LIMIT) exit
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! Count last decimal digit
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EndDigit(mod(idx, 10)) = EndDigit(mod(idx, 10)) + 1
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j = j + 1
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if (j == k) then
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write(*, '(A10,A1,A11,A1)', advance='no') CommaUint(int(j, int64)), '|', CommaUint(int(idx, int64)), '|'
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write(*, '(F7.3,A4)', advance='no') real(EndDigit(1))/j*100, '% |'
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write(*, '(F7.3,A4)', advance='no') real(EndDigit(3))/j*100, '% |'
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write(*, '(F7.3,A4)', advance='no') real(EndDigit(7))/j*100, '% |'
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write(*, '(F7.3,A2)') real(EndDigit(9))/j*100, '%'
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if (k < 100000) then
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k = 100000
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else
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k = k + 100000
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end if
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end if
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idx = idx + 1
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if (j >= 400000) exit
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end do
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print '(/,a,f8.6,1x,a)', 'Elapsed time = ',(yy-xx)/1000.0,'seconds'
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contains
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subroutine Sieve4n_3_Primes(Limit, P4n3)
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use iso_fortran_env
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integer(int32), intent(in) :: Limit
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integer(int32), allocatable, intent(out) :: P4n3(:)
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integer(kind=1), allocatable :: sieve(:)
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integer(int32) :: BlPrCnt, idx, n, j, sieve_size
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sieve_size = (Limit / 3 - 3) / 4 + 1
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allocate(sieve(0:sieve_size-1))
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allocate(P4n3(0:sieve_size-1))
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sieve = 0
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BlPrCnt = 0
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idx = 0
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do
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if (sieve(idx) == 0) then
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n = idx*4 + 3
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P4n3(BlPrCnt) = n
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BlPrCnt = BlPrCnt + 1
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j = idx + n
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if (j > ubound(sieve, 1)) exit
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do while (j <= ubound(sieve, 1))
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sieve(j) = 1
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j = j + n
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end do
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end if
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idx = idx + 1
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if (idx > ubound(sieve, 1)) exit
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end do
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! Collect the rest
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do idx = idx, ubound(sieve, 1)
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if (sieve(idx) == 0) then
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P4n3(BlPrCnt) = idx*4 + 3
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BlPrCnt = BlPrCnt + 1
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end if
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end do
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P4n3 = P4n3(0:BlPrCnt-1)
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end subroutine Sieve4n_3_Primes
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function CommaUint(n) result(res)
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integer, parameter :: sizer = 30
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integer(int64), intent(in) :: n
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character(:), allocatable :: res
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character(len=sizer) :: temp
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integer :: fromIdx, toIdx, i
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character :: pRes(sizer)
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write(temp, '(I0)') n
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fromIdx = len_trim(temp)
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toIdx = fromIdx - 1
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if (toIdx < 3) then
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res = temp(1:fromIdx)
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return
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end if
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allocate(res, mold=repeat(' ',sizer))
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toIdx = 4*(toIdx / 3) + mod(toIdx, 3) + 1
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pRes = ' '
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do i = 1, fromIdx
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pRes(toIdx) = temp(fromIdx-i+1:fromIdx-i+1)
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toIdx = toIdx - 1
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if (mod(i, 3) == 0 .and. i /= fromIdx) then
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pRes(toIdx) = ','
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toIdx = toIdx - 1
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end if
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end do
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do i = 1,sizer ! Go from character array to string
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res(I:I) = pRes(i)
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end do
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!
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res = trim(adjustl(Res))
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end function CommaUint
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end program BlumInteger
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@ -1,39 +1,76 @@
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Dim Shared As Uinteger Prime1
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Dim As Uinteger n = 3, c = 0, Prime2
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#include "isprime.bas"
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Function isSemiprime(n As Uinteger) As Boolean
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Dim As Uinteger d = 3, c = 0
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While d*d <= n
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While n Mod d = 0
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If c = 2 Then Return False
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n /= d
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c += 1
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Wend
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d += 2
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Wend
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Prime1 = n
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Return c = 1
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Type PrimeHelper
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inc(7) As Integer
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idx As Integer
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End Type
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Function initPrimeHelper() As PrimeHelper
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Dim helper As PrimeHelper
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helper.inc(0) = 4 : helper.inc(1) = 2 : helper.inc(2) = 4
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helper.inc(3) = 2 : helper.inc(4) = 4 : helper.inc(5) = 6
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helper.inc(6) = 2 : helper.inc(7) = 6
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helper.idx = 0
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Return helper
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End Function
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Print "The first 50 Blum integers:"
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Do
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If isSemiprime(n) Then
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If Prime1 Mod 4 = 3 Then
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Prime2 = n / Prime1
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If (Prime2 <> Prime1) And (Prime2 Mod 4 = 3) Then
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c += 1
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If c <= 50 Then
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Print Using "####"; n;
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If c Mod 10 = 0 Then Print
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End If
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If c >= 26828 Then
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Print !"\nThe 26828th Blum integer is: " ; n
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Exit Do
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Function firstPrimeFactor(n As Integer) As Integer
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If n = 1 Then Return 1
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If n Mod 3 = 0 Then Return 3
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If n Mod 5 = 0 Then Return 5
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Dim helper As PrimeHelper = initPrimeHelper()
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Dim k As Integer = 7
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While k * k <= n
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If n Mod k = 0 Then Return k
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k += helper.inc(helper.idx)
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helper.idx = (helper.idx + 1) Mod 8
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Wend
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Return n
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End Function
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Sub main()
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Dim As Integer blum(49), counts(9)
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Dim As Integer bc = 0, i = 1, p, q
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Dim As Integer j
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Dim As Double t0 = Timer
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Do
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p = firstPrimeFactor(i)
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If p Mod 4 = 3 Then
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q = i \ p
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If q <> p Andalso q Mod 4 = 3 Andalso isPrime(q) Then
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If bc < 50 Then blum(bc) = i
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counts(i Mod 10) += 1
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bc += 1
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If bc = 50 Then
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Print "First 50 Blum integers:"
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For j = 0 To 49
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Print Using "####"; blum(j);
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If (j + 1) Mod 10 = 0 Then Print
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Next
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Print
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Elseif bc = 26828 Orelse bc Mod 100000 = 0 Then
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Print Using "The ###,###th Blum integer is: #,###,###"; bc; i
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If bc = 400000 Then
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Print !"\n% distribution of the first 400,000 Blum integers:"
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For j = 1 To 9 Step 2
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If j <> 5 Then Print Using " ##.###% end in #"; (counts(j)/4000); j
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Next
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Exit Do
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End If
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End If
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End If
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End If
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End If
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n += 2
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Loop
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i += Iif(i Mod 5 = 3, 4, 2)
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Loop
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Print Chr(10); Timer - t0; " sec."
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End Sub
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main()
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Sleep
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@ -1,44 +1,67 @@
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Public Prime1 As Integer
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Use "isprime.bas"
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Public Sub Main()
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Private inc As Integer[] = [4, 2, 4, 2, 4, 6, 2, 6]
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Dim n As Integer = 3, c As Integer = 0, Prime2 As Integer
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Private Function FirstPrimeFactor(n As Long) As Long
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Print "The first 50 Blum integers:"
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Do
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If isSemiprime(n) Then
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If Prime1 Mod 4 = 3 Then
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Prime2 = n / Prime1
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If (Prime2 <> Prime1) And (Prime2 Mod 4 = 3) Then
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c += 1
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If c <= 50 Then
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Print Format$(n, "####");
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If c Mod 10 = 0 Then Print
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End If
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If c >= 26828 Then
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Print "\nThe 26828th Blum integer is: "; n
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Break
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End If
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End If
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End If
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End If
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n += 2
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Loop
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If n = 1 Then Return 1
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If n Mod 3 = 0 Then Return 3
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If n Mod 5 = 0 Then Return 5
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Dim k As Long = 7
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Dim i As Integer = 0
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While k * k <= n
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If n Mod k = 0 Then Return k
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k += inc[i]
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i = (i + 1) Mod 8
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Wend
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Return n
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End
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Function isSemiprime(n As Integer) As Boolean
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Public Sub Main()
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Dim d As Integer = 3, c As Integer = 0
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While d * d <= n
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While n Mod d = 0
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If c = 2 Then Return False
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n /= d
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c += 1
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Wend
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d += 2
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Dim blum As New Long[50]
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Dim counts As New Collection
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counts[1] = 0
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counts[3] = 0
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counts[7] = 0
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counts[9] = 0
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Dim bc As Long = 0, i As Long = 1
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While True
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Dim p As Long = FirstPrimeFactor(i)
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If p Mod 4 = 3 Then
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Dim q As Long = i \ p
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If q <> p And q Mod 4 = 3 And IsPrime(q) Then
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If bc < 50 Then blum[bc] = i
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counts[i Mod 10] += 1
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bc += 1
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If bc = 50 Then
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Print "First 50 Blum integers:"
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For j As Integer = 0 To 49
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Print Format(blum[j], "####"); " ";
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If (j + 1) Mod 10 = 0 Then Print
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Next
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Print
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Else If bc = 26828 Or bc Mod 100000 = 0 Then
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Print "The "; Format(bc, " ###,###"); "th Blum integer is: "; Format(i, " #,###,###")
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If bc = 400000 Then
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Print Chr(10); "% distribution of the first 400,000 Blum integers:"
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For Each j As Integer In [1, 3, 7, 9]
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Print Format(counts[j] / 4000, " ##.###"); "% end in "; j
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Next
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Return
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Endif
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Endif
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Endif
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Endif
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i += If(i Mod 5 = 3, 4, 2)
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Wend
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Prime1 = n
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Return c = 1
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End Function
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End
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78
Task/Blum-integer/OxygenBasic/blum-integer.basic
Normal file
78
Task/Blum-integer/OxygenBasic/blum-integer.basic
Normal file
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@ -0,0 +1,78 @@
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#include "isprime.bas"
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uses console
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dim inc(7) as integer
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inc(0) = 4: inc(1) = 2: inc(2) = 4
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inc(3) = 2: inc(4) = 4: inc(5) = 6
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inc(6) = 2: inc(7) = 6
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function firstPrimeFactor(n as long) as long
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if n = 1 then return 1
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if n mod 3 = 0 then return 3
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if n mod 5 = 0 then return 5
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||||
|
||||
long k = 7
|
||||
int idx = 0
|
||||
|
||||
while k * k <= n
|
||||
if mod(n, k) = 0 then return k
|
||||
k += inc(idx)
|
||||
idx = mod((idx + 1), 8)
|
||||
wend
|
||||
return n
|
||||
end function
|
||||
|
||||
sub main()
|
||||
dim as long blum(49), counts(9)
|
||||
long bc = 0, i = 1, pct, p, q
|
||||
int j
|
||||
string s, t
|
||||
|
||||
do
|
||||
p = firstPrimeFactor(i)
|
||||
if p mod 4 = 3 then
|
||||
q = i \ p
|
||||
if q <> p and q mod 4 = 3 and isPrime(q) then
|
||||
if bc < 50 then blum(bc) = i
|
||||
counts(i mod 10) = counts(i mod 10) + 1
|
||||
bc += 1
|
||||
|
||||
if bc = 50 then
|
||||
printl "First 50 Blum integers:"
|
||||
for j = 0 to 49
|
||||
s = str(blum(j))
|
||||
while len(s) < 4: s = " " + s: wend
|
||||
print s;
|
||||
if mod((j + 1), 10) = 0 then printl
|
||||
next
|
||||
printl
|
||||
elseif bc = 26828 or bc mod 100000 = 0 then
|
||||
s = str(bc)
|
||||
while len(s) < 6: s = " " + s: wend
|
||||
t = str(i)
|
||||
while len(t) < 7: t = " " + t: wend
|
||||
printl "The " + s + "th Blum integer is: " + t
|
||||
if bc = 400000 then
|
||||
printl cr "% distribution of the first 400,000 Blum integers:"
|
||||
|
||||
for j = 1 to 9 step 2
|
||||
if j <> 5 then
|
||||
pct = counts(j)/4000
|
||||
s = str(pct)
|
||||
while len(s) < 5: s = " " + s: wend
|
||||
printl s + "% end in " + str(j)
|
||||
end if
|
||||
next
|
||||
end
|
||||
end if
|
||||
end if
|
||||
end if
|
||||
end if
|
||||
if mod(i, 5) = 3 then i += 4 else i += 2
|
||||
end do
|
||||
end sub
|
||||
|
||||
main()
|
||||
|
||||
printl cr "Enter ..."
|
||||
waitkey
|
||||
69
Task/Blum-integer/PureBasic/blum-integer.basic
Normal file
69
Task/Blum-integer/PureBasic/blum-integer.basic
Normal file
|
|
@ -0,0 +1,69 @@
|
|||
XIncludeFile "isprime.pb"
|
||||
|
||||
Structure PrimeHelper
|
||||
inc.i[8]
|
||||
index.i
|
||||
EndStructure
|
||||
|
||||
Procedure.i firstPrimeFactor(n.q)
|
||||
If n = 1 : ProcedureReturn 1 : EndIf
|
||||
If n % 3 = 0 : ProcedureReturn 3 : EndIf
|
||||
If n % 5 = 0 : ProcedureReturn 5 : EndIf
|
||||
|
||||
Define helper.PrimeHelper
|
||||
helper\inc[0] = 4 : helper\inc[1] = 2 : helper\inc[2] = 4
|
||||
helper\inc[3] = 2 : helper\inc[4] = 4 : helper\inc[5] = 6
|
||||
helper\inc[6] = 2 : helper\inc[7] = 6
|
||||
|
||||
Define k.q = 7
|
||||
While k * k <= n
|
||||
If n % k = 0 : ProcedureReturn k : EndIf
|
||||
k + helper\inc[helper\index]
|
||||
helper\index = (helper\index + 1) % 8
|
||||
Wend
|
||||
ProcedureReturn n
|
||||
EndProcedure
|
||||
|
||||
OpenConsole()
|
||||
Define Dim blum.q(49)
|
||||
Define.q bc = 0, i = 1
|
||||
Define Dim counts.q(9)
|
||||
|
||||
Repeat
|
||||
Define p.q = firstPrimeFactor(i)
|
||||
If p % 4 = 3
|
||||
Define q.q = i / p
|
||||
If q <> p And q % 4 = 3 And isPrime(q)
|
||||
If bc < 50 : blum(bc) = i : EndIf
|
||||
counts(i % 10) + 1
|
||||
bc + 1
|
||||
|
||||
If bc = 50
|
||||
PrintN("First 50 Blum integers:")
|
||||
For j = 0 To 49
|
||||
Print(" " + RSet(Str(blum(j)), 3))
|
||||
If (j + 1) % 10 = 0 : PrintN("") : EndIf
|
||||
Next
|
||||
PrintN("")
|
||||
ElseIf bc = 26828 Or bc % 100000 = 0
|
||||
PrintN("The " + RSet(Str(bc), 6) + "th Blum integer is: " + RSet(Str(i), 7))
|
||||
If bc = 400000
|
||||
PrintN(#CRLF$ + "% distribution of the first 400,000 Blum integers:")
|
||||
For j = 1 To 9 Step 2
|
||||
If j <> 5
|
||||
PrintN(RSet(StrF(counts(j)/4000, 3), 5) + "% end in " + Str(j))
|
||||
EndIf
|
||||
Next
|
||||
Break
|
||||
EndIf
|
||||
EndIf
|
||||
EndIf
|
||||
EndIf
|
||||
If i % 5 = 3
|
||||
i + 4
|
||||
Else
|
||||
i + 2
|
||||
EndIf
|
||||
ForEver
|
||||
|
||||
PrintN(#CRLF$ + "Press ENTER to exit"): Input()
|
||||
73
Task/Blum-integer/QB64/blum-integer.qb64
Normal file
73
Task/Blum-integer/QB64/blum-integer.qb64
Normal file
|
|
@ -0,0 +1,73 @@
|
|||
Dim Shared inc(7) As Integer
|
||||
inc(0) = 4: inc(1) = 2: inc(2) = 4
|
||||
inc(3) = 2: inc(4) = 4: inc(5) = 6
|
||||
inc(6) = 2: inc(7) = 6
|
||||
|
||||
Dim blum(49) As Long
|
||||
Dim counts(9) As Long
|
||||
Dim bc As Long, i As Long, p As Long, q As Long, j As Integer
|
||||
i = 1
|
||||
|
||||
Do
|
||||
p = firstPrimeFactor(i)
|
||||
If p Mod 4 = 3 Then
|
||||
q = i \ p
|
||||
If q <> p And q Mod 4 = 3 And isPrime(q) Then
|
||||
If bc < 50 Then blum(bc) = i
|
||||
counts(i Mod 10) = counts(i Mod 10) + 1
|
||||
bc = bc + 1
|
||||
|
||||
If bc = 50 Then
|
||||
Print "First 50 Blum integers:"
|
||||
For j = 0 To 49
|
||||
Print Using "####"; blum(j);
|
||||
If (j + 1) Mod 10 = 0 Then Print
|
||||
Next
|
||||
Print
|
||||
ElseIf bc = 26828 Or bc Mod 100000 = 0 Then
|
||||
Print Using "The ###,###th Blum integer is: #,###,###"; bc; i
|
||||
If bc = 400000 Then
|
||||
Print Chr$(10); "% distribution of the first 400,000 Blum integers:"
|
||||
For j = 1 To 9 Step 2
|
||||
If j <> 5 Then
|
||||
Print Using " ##.###% end in #"; (counts(j%) / 4000); j%
|
||||
End If
|
||||
Next
|
||||
End
|
||||
End If
|
||||
End If
|
||||
End If
|
||||
End If
|
||||
If i Mod 5 = 3 Then i = i + 4 Else i = i + 2
|
||||
Loop
|
||||
End
|
||||
|
||||
Function firstPrimeFactor& (n As Long)
|
||||
Dim k As Long, idx As Integer
|
||||
If n = 1 Then firstPrimeFactor& = 1: Exit Function
|
||||
If n Mod 3 = 0 Then firstPrimeFactor& = 3: Exit Function
|
||||
If n Mod 5 = 0 Then firstPrimeFactor& = 5: Exit Function
|
||||
k = 7: idx = 0
|
||||
Do While k * k <= n
|
||||
If n Mod k = 0 Then
|
||||
firstPrimeFactor& = k
|
||||
Exit Function
|
||||
End If
|
||||
k = k + inc(idx)
|
||||
idx = (idx + 1) Mod 8
|
||||
Loop
|
||||
firstPrimeFactor& = n
|
||||
End Function
|
||||
|
||||
Function isPrime% (n As Long)
|
||||
Dim i As Long
|
||||
If n <= 1 Then Exit Function
|
||||
If n <= 3 Then isPrime% = 1: Exit Function
|
||||
If n Mod 2 = 0 Or n Mod 3 = 0 Then Exit Function
|
||||
i = 5
|
||||
While i * i <= n
|
||||
If n Mod i = 0 Or n Mod (i + 2) = 0 Then Exit Function
|
||||
i = i + 6
|
||||
Wend
|
||||
isPrime% = 1
|
||||
End Function
|
||||
Loading…
Add table
Add a link
Reference in a new issue