Prime p₀= 2718216453902162867 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 40 2 64 2 40 2 28 2 16 2 (?)
a_n: 0 2 12 14 54 56 120 122 162 164 192 194 210 212
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: 212
Found by: [SG-FC] hl
db: batch=82, k=14, 10 40 64 40 28 16

SPT(16)	2718215578265105221	0 6 10 76 118 132 156 196 342 382 406 420 462 528 532 538	-875637057646
SPT(16)	2718215680721914081	0 52 60 66 70 90 106 108 130 132 148 168 172 178 186 238	-773180248786
SPT(16)	2718215808847554451	0 16 18 28 88 102 106 130 168 192 196 210 270 280 282 298	-645054608416
SPT(16)	2718215901813383857	0 4 6 34 72 84 100 114 142 156 172 184 222 250 252 256	-552088779010
SPT(16)	2718216114638752033	0 34 54 60 70 76 150 166 174 190 264 270 280 286 306 340	-339263410834
SPT(16)	2718216426008955679	0 40 64 78 90 132 168 192 220 244 280 322 334 348 372 412	-27893207188
STPT(10)	2718216555732557819	0 2 18 20 60 62 102 104 120 122	101830394952
STPT(10)	2718217209302725157	0 2 24 26 42 44 60 62 84 86	755400562290
STPT(10)	2718217303902397397	0 2 42 44 72 74 102 104 144 146	850000234530
SPT(16)	2718217562425060253	0 50 84 90 96 134 138 140 174 176 180 218 224 230 264 314	1108522897386
SPT(16)	2718217757291417681	0 42 66 102 128 146 182 198 200 216 252 270 296 332 356 398	1303389254814