Least lower twin prime p such the the sum of the distances to adjacent primes is a new record.
3, 5, 11, 29, 137, 419, 521, 1151, 1931, 1949, 6449, 10007, 28349, 35729, 48731, 85931, 107507, 173429, 838247, 1349531, 3593201, 29187407, 53231051, 70396589, 83528411, 191186249, 555142307, 1301756411
1
That is, we sum the distances of p to the next lower prime and p+2 to the next higher prime.
T. D. Noe, Plot of 28 terms
Eric W. Weisstein, MathWorld: Twin Primes
(Mma) tp = Reap[Do[p = Prime[i]; If[PrimeQ[p + 2], Sow[p]], {i, PrimePi[2000000]}]][[2, 1]]; t = {{3, 3, 1, 2}}; Do[s = {tp[[n]] - Prime[PrimePi[tp[[n]]] - 1], Prime[PrimePi[tp[[n]] + 2] + 1] - tp[[n]] - 2}; If[s[[1]] + s[[2]] > t[[-1, 2]], AppendTo[t, {tp[[n]], s[[1]] + s[[2]], s[[1]], s[[2]]}]], {n, Length[tp]}]; Transpose[t][[1]]
nonn,more
T. D. Noe, Nov 26 2015