Prime p₀= 1126371979147882529 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 118 2 16 2 58 2 10 2 (?)
a_n: 0 2 30 32 72 74 192 194 210 212 270 272 282 284
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: 284
Found by: crashtech
db: batch=76, k=14, 28 40 118 16 58 10

SPT(18)	1126371174942903353	0 24 44 60 150 168 188 234 336 398 500 546 566 584 674 690 710 734	-804204979176
SPT(16)	1126371216300224303	0 14 44 68 90 128 156 170 234 248 276 314 336 360 390 404	-762847658226
STPT(10)	1126371435310235339	0 2 78 80 120 122 162 164 240 242	-543837647190
STPT(10)	1126371451724413589	0 2 30 32 60 62 90 92 120 122	-527423468940
SPT(16)	1126371533590285453	0 4 18 30 64 100 106 150 154 198 204 240 274 286 300 304	-445557597076
STPT(12)	1126371727243173737	0 2 30 32 42 44 132 134 144 146 174 176	-251904708792
STPT(10)	1126372035341814881	0 2 6 8 48 50 90 92 96 98	56193932352
SPT(16)	1126372315689931991	0 18 30 48 80 132 158 192 248 282 308 360 392 410 422 440	336542049462
STPT(10)	1126372445473947569	0 2 18 20 30 32 42 44 60 62	466326065040
STPT(10)	1126372627067297459	0 2 48 50 90 92 132 134 180 182	647919414930
SPT(16)	1126372698666859927	0 22 24 54 82 106 112 136 150 174 180 204 232 262 264 286	719518977398