Prime p₀= 1144371627513153539 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 28 2 10 2 196 2 112 2 154 2 (?)
a_n: 0 2 78 80 108 110 120 122 318 320 432 434 588 590
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: 590
Found by: Putin Has a Small Dick
db: batch=76, k=14, 76 28 10 196 112 154

SPT(16)	1144370789709305671	0 22 52 76 120 172 178 190 258 270 276 328 372 396 426 448	-837803847868
SPT(16)	1144370844790841771	0 8 12 36 42 68 98 126 152 180 210 236 242 266 270 278	-782722311768
TPT(14)	1144370873145682319	0 2 18 20 60 62 210 212 222 224 258 260 282 284	-754367471220
TPT(14)	1144371251137879907	0 2 42 44 102 104 132 134 174 176 204 206 312 314	-376375273632
STPT(10)	1144371383406553187	0 2 30 32 42 44 54 56 84 86	-244106600352
SPT(16)	1144371609583913987	0 12 66 72 86 96 110 156 176 222 236 246 260 266 320 332	-17929239552
SPT(16)	1144371920043958747	0 4 10 42 60 84 130 144 190 204 250 274 292 324 330 334	292530805208
SPT(16)	1144371960948828809	0 30 38 98 108 134 140 200 288 348 354 380 390 450 458 488	333435675270
TPT(14)	1144372371121557887	0 2 84 86 114 116 150 152 210 212 282 284 540 542	743608404348
SPT(16)	1144372449475653917	0 2 36 56 72 120 122 126 206 210 212 260 276 296 330 332	821962500378
SPT(16)	1144373081148492277	0 24 46 64 66 96 106 130 210 234 244 274 276 294 316 340	1453635338738