Prime p₀= 2735997936775012757 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 28 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 72 74 84 86
All 10 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 86
Found by: fix
db: batch=82, k=10, 2 10 2 28 2

SPT(16)	2735996769486553843	0 40 78 114 124 144 180 210 244 274 310 330 340 376 414 454	-1167288458914
SPT(16)	2735996963510318867	0 2 20 24 50 66 80 90 116 126 140 156 182 186 204 206	-973264693890
STPT(10)	2735997135388448759	0 2 18 20 60 62 102 104 120 122	-801386563998
SPT(16)	2735997210896793017	0 6 26 42 66 72 84 110 186 212 224 230 254 270 290 296	-725878219740
STPT(10)	2735997267944528639	0 2 18 20 60 62 102 104 120 122	-668830484118
SPT(16)	2735997306485744641	0 6 16 36 88 90 112 222 316 426 448 450 502 522 532 538	-630289268116
TPT(14)	2735998081896233771	0 2 36 38 66 68 108 110 126 128 168 170 288 290	145121221014
STPT(10)	2735998356609519047	0 2 54 56 72 74 90 92 144 146	419834506290
SPT(16)	2735998373658191951	0 30 66 72 78 96 108 122 156 170 182 200 206 212 248 278	436883179194
STPT(10)	2735998783049188211	0 2 36 38 78 80 120 122 156 158	846274175454
STPT(10)	2735999276455412447	0 2 30 32 42 44 54 56 84 86	1339680399690