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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,
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]));{}
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

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]));{}
until 1<0;
END;
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