Prime p₀= 2549512324471806431 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 28 2 28 2 10 2 106 2 46 2 (?)
a_n: 0 2 108 110 138 140 168 170 180 182 288 290 336 338
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: 338
Found by: JayPi
db: batch=82, k=14, 106 28 28 10 106 46

STPT(10)	2549509816004603951	0 2 36 38 78 80 120 122 156 158	-2508467202480
TPT(14)	2549510248702272047	0 2 12 14 84 86 150 152 174 176 264 266 330 332	-2075769534384
SPT(16)	2549510455326967579	0 10 24 30 84 102 154 172 222 240 292 310 364 370 384 394	-1869144838852
SPT(16)	2549510951837363831	0 80 92 102 116 150 176 218 240 282 308 342 356 366 378 458	-1372634442600
STPT(10)	2549512022976726989	0 2 18 20 30 32 42 44 60 62	-301495079442
SPT(16)	2549512171166153077	0 10 16 34 52 100 132 154 162 184 216 264 282 300 306 316	-153305653354
SPT(16)	2549512435771398467	0 2 84 90 104 132 186 252 284 350 404 432 446 452 534 536	111299592036
SPT(16)	2549512702351258453	0 6 24 40 118 130 138 150 154 166 174 186 264 280 298 304	377879452022
STPT(10)	2549512869944644577	0 2 30 32 120 122 210 212 240 242	545472838146
STPT(10)	2549513143704045809	0 2 42 44 90 92 138 140 180 182	819232239378
SPT(16)	2549513218949671757	0 12 24 30 102 110 116 122 144 150 156 164 236 242 254 266	894477865326