Prime p₀= 1437767906388523277 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 58 2 250 2 148 2 16 2 40 2 (?)
a_n: 0 2 12 14 72 74 324 326 474 476 492 494 534 536
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: 536
Found by: JagDoc
db: batch=78, k=14, 10 58 250 148 16 40

SPT(16)	1437767010391827811	0 16 36 70 90 112 142 178 180 216 246 268 288 322 342 358	-895996695466
SPT(16)	1437767015229394547	0 32 92 102 162 174 210 224 312 326 362 374 434 444 504 536	-891159128730
SPT(16)	1437767086319577007	0 10 16 22 82 130 144 154 222 232 246 294 354 360 366 376	-820068946270
SPT(16)	1437767110918772671	0 6 42 48 60 70 76 160 168 252 258 268 280 286 322 328	-795469750606
SPT(16)	1437767621372136931	0 22 30 70 76 106 126 132 136 142 162 192 198 238 246 268	-285016386346
TPT(14)	1437767786776219487	0 2 24 26 30 32 120 122 180 182 210 212 240 242	-119612303790
STPT(10)	1437768041011793549	0 2 42 44 60 62 78 80 120 122	134623270272
SPT(16)	1437768398688013739	0 20 32 44 54 68 98 114 158 174 204 218 228 240 252 272	492299490462
SPT(16)	1437768448571003957	0 2 6 30 36 42 44 50 126 132 134 140 146 170 174 176	542182480680
SPT(16)	1437768689177514059	0 32 98 108 150 170 182 218 234 270 282 302 344 354 420 452	782788990782
STPT(10)	1437769214799651917	0 2 30 32 42 44 54 56 84 86	1308411128640