Prime p₀= 1281141358343691431 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 64 2 88 2 10 2 10 2 166 2 (?)
a_n: 0 2 30 32 96 98 186 188 198 200 210 212 378 380
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: 380
Found by: vaughan
db: batch=77, k=14, 28 64 88 10 10 166

STPT(12)	1281139129722765431	0 2 18 20 60 62 66 68 108 110 126 128	-2228620926000
STPT(10)	1281139869313457927	0 2 54 56 72 74 90 92 144 146	-1489030233504
SPT(16)	1281140443476421769	0 2 14 30 72 114 140 168 194 222 248 290 332 348 360 362	-914867269662
STPT(10)	1281140513649659417	0 2 42 44 72 74 102 104 144 146	-844694032014
STPT(10)	1281140828342623361	0 2 36 38 78 80 120 122 156 158	-530001068070
SPT(16)	1281141105624525701	0 6 8 48 56 86 90 140 156 206 210 240 248 288 290 296	-252719165730
SPT(16)	1281141563324025413	0 48 50 86 108 128 258 260 294 296 426 446 468 504 506 554	204980333982
SPT(16)	1281141584370973667	0 12 42 62 90 110 114 156 170 212 216 236 264 284 314 326	226027282236
SPT(16)	1281141656056715419	0 10 40 42 54 84 94 120 142 168 178 208 220 222 252 262	297713023988
STPT(10)	1281142741813325747	0 2 30 32 72 74 114 116 144 146	1383469634316
SPT(16)	1281142743923326201	0 58 78 120 142 168 190 196 222 228 250 276 298 340 360 418	1385579634770