Hardy-Littlewood Twin Prime Conjecture

Twin prime constant is 2 C2, where 
C2 = Prod_{p > 2} p(p-2) / (p-1)^2 =approx= .660161815846

hl[x_] := .660161815846  * 2 *x / (Log[x] Log[x]);
hl2[x_]  := .660161815846  * 2 * NIntegrate[1/(Log[t] Log[t]), {t,2,x}]

twins = {};
p1 = 2;
numtwins = 0;
hlguess = {};
hl2guess = {};
diff = {};
normdiff = {};
numdo =600000;
For[j=2, j ≤ numdo, j++,
{
p2 = Prime[j];
If[p2 - p1 == 2, 
{
numtwins  = numtwins + 1;
twins = AppendTo[twins, {p1,numtwins}];
hlguess = AppendTo[hlguess, {p1,hl[p1]}];
hl2temp = hl2[p1];
hl2guess = AppendTo[hl2guess, {p1,hl2temp}];
diff = AppendTo[diff, {p1, (numtwins - hl2[p1])}];
normdiff = AppendTo[normdiff, {p1, (numtwins - hl2temp)/numtwins}];
}];
p1 = p2;
}];
Print["Number of twin primes up to ", Prime[numdo], " is ",numtwins];
Print["Main term of prediction is: ",hl[Prime[numdo]]];
Print["Full prediction is: ", hl2[Prime[numdo]]];
ListPlot[{twins,hlguess}]
Print["Plot of twin primes versus main term of prediction."];
Print[" "];
ListPlot[{twins,hl2guess}]
Print["Plot of twin primes versus full prediction."];
Print[ListPlot[diff]];
Print["Plot of difference of observed - full prediction."]; 
Print[ListPlot[normdiff]];
Print["Plot of difference of observed - full prediction divided by number observed."];