Prime p₀= 1267963360812480251 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 88 2 10 2 28 2 40 2 4 2 (?)
a_n: 0 2 36 38 126 128 138 140 168 170 210 212 216 218
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: 218
Found by: Megacruncher
db: batch=77, k=14, 34 88 10 28 40 4

SPT(16)	1267961591337066721	0 6 12 40 46 58 88 142 156 210 240 252 258 286 292 298	-1769475413530
SPT(16)	1267961712101501107	0 6 22 36 42 54 66 124 132 190 202 214 220 234 250 256	-1648710979144
SPT(16)	1267962072009063857	0 2 24 32 44 54 84 122 132 170 200 210 222 230 252 254	-1288803416394
STPT(10)	1267962723963568151	0 2 36 38 78 80 120 122 156 158	-636848912100
STPT(10)	1267963028135746247	0 2 30 32 42 44 54 56 84 86	-332676734004
SPT(16)	1267963069334856959	0 18 72 78 114 122 128 168 284 324 330 338 374 380 434 452	-291477623292
SPT(16)	1267963475123720917	0 40 64 66 84 106 120 150 196 226 240 262 280 282 306 346	114311240666
STPT(10)	1267963486621810871	0 2 6 8 48 50 90 92 96 98	125809330620
SPT(18)	1267963498670866027	0 4 34 52 76 106 150 154 172 174 192 196 240 270 294 312 342 346	137858385776
SPT(16)	1267964075898281309	0 18 38 48 60 62 72 132 158 218 228 230 242 252 272 290	715085801058
SPT(16)	1267964282705285093	0 24 66 68 108 110 144 164 180 200 234 236 276 278 320 344	921892804842