Prime p₀= 2681551812190309781 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 94 2 40 2 28 2 10 2 (?)
a_n: 0 2 60 62 90 92 186 188 228 230 258 260 270 272
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 272
Found by: [SG-FC] hl
db: batch=82, k=14, 58 28 94 40 28 10

SPT(16)	2681550957400226101	0 28 36 58 72 78 82 102 106 126 130 136 150 172 180 208	-854790083680
STPT(10)	2681551006207167971	0 2 30 32 60 62 90 92 120 122	-805983141810
SPT(16)	2681551051056484333	0 34 70 84 96 126 138 178 216 256 268 298 310 324 360 394	-761133825448
SPT(16)	2681551552068878743	0 16 30 48 78 88 100 126 190 216 228 238 268 286 300 316	-260121431038
STPT(10)	2681551695329176847	0 2 72 74 102 104 132 134 204 206	-116861132934
SPT(16)	2681551803490856617	0 52 60 96 142 154 210 214 222 226 282 294 340 376 384 436	-8699453164
STPT(10)	2681552504927082131	0 2 36 38 78 80 120 122 156 158	692736772350
STPT(12)	2681552955764111267	0 2 12 14 54 56 60 62 102 104 114 116	1143573801486
TPT(14)	2681552999399358011	0 2 48 50 90 92 96 98 228 230 306 308 366 368	1187209048230
SPT(16)	2681553500658480377	0 14 24 26 80 86 90 140 156 206 210 216 270 272 282 296	1688468170596
SPT(18)	2681553565288305247	0 114 124 144 154 156 166 190 196 264 270 294 304 306 316 336 346 460	1753097995466