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Prime Chain of 161

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  • aldrich617
    This is a Prime Chain of 161 consecutive terms, including 155 distinct primes, consisting of the output of four well-known prime-producing equations that
    Message 1 of 1 , Jul 21, 2008
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      This is a Prime Chain of 161 consecutive terms, including
      155 distinct primes, consisting of the output of
      four well-known prime-producing equations that
      alternate sequentially within a procedural expression
      of a single polynomial. The equations are:

      -(x^5 - 133x^4 + 6729x^3 - 158379x^2 = 1720294x -6823316)/4,
      42x^3 + 270x^2 -2643x + 250703,
      x^4 - 97x^3 + 3294x^2 -45458x + 213589,
      -(3x^3 - 183x^2 + 3318x - 18757)

      1705829,250703,213589,
      18757,1313781,224579,171329,15619,991127,199247,
      135089,12829,729173,174959,104323,10369,519643,151967,78509,8221,
      355049,130523,57149,6367,228581,110879,39769,4789,134077,93287,
      25919,3469,65993,77999,15173,2389,19373,65267,7129,1531,
      -10181,55343,1409,877,-26539,48479,-2341,409,-33073,44927,
      -4451,109,-32687,44939,-5227,-41,-27847,48767,-4951,-59,
      -20611,56663,-3881,37,-12659,68879,-2251,229,-5323,85667,
      -271,499,383,107279,1873,829,3733,133967,4019,1201,
      4259,165983,6029,1597,1721,203579,7789,1999,-3923,247007,
      9209,2389,-12547,296519,10223,2749,-23887,352367,10789,3061,
      -37571,414803,10889,3307,-53149,484079,10529,3469,-70123,560447,
      9739,3529,-87977,644159,8573,3469,-106207,735467,7109,3271,
      124351,834623,5449,2917,-142019,941879,3719,2389,-158923,1057487,
      2069,1669,-174907,1181699,673,739,-189977,1314767,-271,-419,
      204331,1456943,-541,-1823,-218389,1608479,109,-3491,-232823,1769627,
      1949,-5441,-248587,1940639,5273,-7691,-266947,2121767,10399,-10259,
      -289511

      The Pascal procedure below should run as an import in several
      programming
      environments as is, and produce the provided prime chain.

      procedure Ndegrees7;
      var a : array[0..32] of extended;
      ct: longint;
      n,nh ,i,j : integer;
      ab1,ab2 : extended;
      begin
      for i := 0 to 32 do
      a[i] := 0;
      N := 23;
      a[0] := 1705829 { FIRST TERM OF PRIME CHAIN};
      writeln('1');
      writeln(trunc(a[0]));
      writeln;
      nh := 1;

      a[1] := 250703; ;a[2] := 213589;a[3] := 18757 ;
      a[4] := 1313701; a[5] := 224579; a[6] :=171329;
      a[7] := 15619; a[8] := 991127; a[9] := 199247;
      a[10] := 135089 ;a[11] := 12829 ;
      a[12] := 729173 ; a[13] := 174959; a[14] := 104323 ;
      a[15] := 10369; a[16] := 519643; a[17] := 151967;
      a[18] := 78509;a[19] := 8221; a[20] := 355049 ;
      a[21] :=130523; a[22] := 57149 ; a[23] := 6367 ;

      repeat
      for i := N downto nh do
      begin
      a[i] := a[i] - a[i-1] ;
      IF NH = 3 THEN A[I] := abs(A[I]); {}
      IF NH = 4 THEN A[I] := abs(A[I]); {}
      IF NH = 5 THEN A[I] := abs(A[I]); {}
      IF NH = 6 THEN A[I] := abs(A[I]); {}
      IF NH = 7 THEN A[I] := abs(A[I]); {}
      IF NH = 9 THEN A[I] := abs(A[I]); {}
      IF NH = 10 THEN A[I] := abs(A[I]); {}
      IF NH = 11 THEN A[I] := abs(A[I]); {}
      IF NH = 13 THEN A[I] := abs(A[I]); {}
      IF NH = 14 THEN A[I] := abs(A[I]); {}
      IF NH = 15 THEN A[I] := abs(A[I]); {}
      IF NH = 17 THEN A[I] := abs(A[I]); {}
      IF NH = 19 THEN A[I] := abs(A[I]); {}
      IF NH = 22 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];

      if odd(ct ) then a[23] := -a[23];{}
      for i := N-1 downto 1 do
      begin
      if i = 22 then if ct mod 2 = 1 then a[22] := -a[22];{}
      if ct > 0 then if i = 19 then if
      ct mod 4 = 0 then a[19] := -a[19];{}
      if i = 19 then if ct mod 4 = 3 then a[19] := -a[19];{}
      if i = 17 then if ct mod 2 = 0 then a[17] := -a[17];{}
      if i = 15 then if ct mod 2 = 1 then a[15] := -a[15];{}
      if i = 14 then if ct mod 4 = 1 then a[14] := -a[14];{}
      if i = 14 then if ct mod 4 = 0 then a[14] := -a[14];{}
      if i = 13 then if ct mod 2 = 0 then a[13] := -a[13];{}
      if i = 11 then if ct mod 2 = 1 then a[11] := -a[11];{}
      if i = 10 then if ct mod 4 <> 1 then a[10] := -a[10];{}
      if i = 9 then if ct mod 2 = 1 then a[9] := -a[9];{}
      if i = 7 then if ct mod 4 = 1 then a[7] := -a[7];{}
      if i = 7 then if ct mod 4 = 0 then a[7] := -a[7];{}
      if i = 6 then if ct mod 4 = 1 then a[6] := -a[6];{}
      if i = 6 then if ct mod 4 = 0 then a[6] := -a[6];{}
      if i = 5 then if ct mod 2 = 0 then a[5] := -a[5];{}
      if i = 4 then if ct mod 4 = 0 then a[4] := -a[4];{}
      if i = 4 then if ct mod 4 = 3 then a[4] := -a[4];{}
      if i = 3 then if ct mod 2 = 1 then a[3] := -a[3];{}

      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;

      Aldrich Stevens
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