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Prime Chain of 100.

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  • aldrich617
    This chain is based on an equation I believe I saw here at the Prime Numbers website last year. 213589,247889,171329,201973,135089,162359,104323,128489,78509,
    Message 1 of 1 , Jun 2, 2008
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      This chain is based on an equation I believe I saw
      here at the Prime Numbers website last year.

      213589,247889,171329,201973,135089,162359,104323,128489,78509,
      99829,57149,75869...

      This is a Prime Chain of 100 terms consisting of the output of
      x^4 - 97x^3 + 3294x^2 -45458x + 213589 alternating with those
      same values in reverse order.

      The Pascal Procedure below used to generate it
      can be imported into Borland's
      latest programming software and should run.

      procedure Ndegrees2;
      var a : array[0..16] of extended;
      ct: longint;
      n,nh ,i,j : integer;
      ab1,ab2 : extended;
      begin
      for i := 0 to 16 do
      a[i] := 0;
      N := 8;
      a[0] := 213589{ FIRST TERM OF PRIME CHAIN};
      writeln('1');
      writeln(trunc(a[0]));
      writeln;
      nh := 1;
      a[1] := 247889 ;a[2] := 171329 ;a[3] := 201973 ;
      a[4] := 135089 ;a[5] := 162359 ;a[6] := 104323;
      a[7] := 128489 ;a[8] := 78509 ; ;

      repeat
      for i := N downto nh do
      begin
      a[i] := a[i] - a[i-1] ;
      IF NH = 5 THEN A[I] := ABS(A[I]); {******}
      End;
      nh := nh + 1;
      until nh = n + 2;
      ct := 0;
      repeat
      ct := ct + 1;
      ab1 := a[n] + a[n-1];
      for i := N-1 downto 1 do
      begin
      IF I = 5 THEN IF ODD(ct + 1) THEN A[i] := -A[i];{******}
      ab2 := a[i] + a[i-1] ;
      a[i] := ab1;
      ab1 := ab2;
      end;
      a[0] := ab1;
      writeln(ct + 1);
      writeln(trunc(a[0]));{}
      READLN;
      until 1<0;
      END;

      There is a small correction to the Prime Chain of 91
      procedure that was posted
      last week in the following message.
      That chain was based on equation
      from David Broadhurst ..

      This is a Prime Chain of 91 terms consisting of the output of
      36x^2 - 810x +2753 alternating with those of the output of its
      first transform 9x^2 -423x + 3167.

      3167,2753,2753,1979,2357,1277,1979,647,1619,89,1277...

      procedure Ndegrees;
      var a : array[0..16] of extended;
      ct: longint;
      n,nh ,i,j : integer;
      ab1,ab2 : extended;
      begin
      for i := 0 to 16 do
      a[i] := 0;
      N := 7;
      a[0] := 3167{ FIRST TERM OF PRIME CHAIN};
      writeln('1');
      writeln(trunc(a[0]));
      writeln;
      nh := 1;
      a[1] := 2753 ;a[2] := 2753 ;a[3] := 1979 ;a[4] := 2357
      ;a[5] := 1277 ;a[6] := 1979 ;a[7] := 647 ;
      repeat
      for i := N downto nh do
      begin
      a[i] := a[i] - a[i-1] ;
      IF NH = 5 THEN A[I] := ABS(A[I]); {******}
      End;
      nh := nh + 1;
      until nh = n + 2;
      ct := 0;
      repeat
      ct := ct + 1;
      ab1 := a[n] + a[n-1];
      for i := N-1 downto 1 do
      begin
      IF I = 5 THEN IF ODD(ct) THEN A[i] := -A[i];{******}
      ab2 := a[i] + a[i-1] ;
      a[i] := ab1;
      ab1 := ab2;
      end;
      a[0] := ab1;
      writeln(ct + 1);
      writeln(trunc(a[0]));{}
      READLN;
      until 1<0;
      END;
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