Prime p₀= 921644647402619969 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 172 2 34 2 52 2 16 2 40 2 (?)
a_n: 0 2 78 80 252 254 288 290 342 344 360 362 402 404
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: 404
Found by: Theadalus
db: batch=76, k=14, 76 172 34 52 16 40

SPT(16)	921643817978049917	0 2 6 14 32 132 230 234 332 336 434 534 552 560 564 566	-829424570052
STPT(10)	921643894572251897	0 2 54 56 72 74 90 92 144 146	-752830368072
TPT(14)	921643917586737881	0 2 156 158 186 188 228 230 378 380 390 392 648 650	-729815882088
SPT(16)	921643967175810721	0 16 42 52 76 126 160 162 190 192 226 276 300 310 336 352	-680226809248
SPT(16)	921644057070716489	0 14 20 32 44 60 74 90 152 168 182 198 210 222 228 242	-590331903480
SPT(16)	921644264944755511	0 42 46 60 66 108 136 148 150 162 190 232 238 252 256 298	-382457864458
STPT(10)	921644781511670309	0 2 18 20 30 32 42 44 60 62	134109050340
SPT(16)	921645188431283027	0 54 56 90 96 200 204 210 236 242 246 350 356 390 392 446	541028663058
STPT(10)	921645501340969607	0 2 42 44 72 74 102 104 144 146	853938349638
SPT(16)	921645667298350987	0 24 42 70 94 150 172 180 256 264 286 342 366 394 412 436	1019895731018
STPT(10)	921645672271489091	0 2 36 38 108 110 180 182 216 218	1024868869122