Prime p₀= 1130005383231811739 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 82 2 4 2 28 2 112 2 28 2 (?)
a_n: 0 2 78 80 162 164 168 170 198 200 312 314 342 344
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: 344
Found by: stoneageman
db: batch=76, k=14, 76 82 4 28 112 28

SPT(16)	1130003677281038173	0 40 78 124 130 144 148 174 250 276 280 294 300 346 384 424	-1705950773566
STPT(10)	1130003812604419169	0 2 18 20 30 32 42 44 60 62	-1570627392570
STPT(10)	1130004830171591219	0 2 138 140 180 182 222 224 360 362	-553060220520
SPT(16)	1130005099958634859	0 24 40 42 64 94 102 108 124 130 138 168 190 192 208 232	-283273176880
STPT(10)	1130005101818989937	0 2 72 74 102 104 132 134 204 206	-281412821802
SPT(16)	1130005264613341891	0 60 66 88 90 102 112 130 168 186 196 208 210 232 238 298	-118618469848
SPT(18)	1130005871923021081	0 16 48 58 60 76 130 136 150 178 192 198 252 268 270 280 312 328	488691209342
STPT(12)	1130006817176415977	0 2 42 44 120 122 162 164 240 242 282 284	1433944604238
SPT(16)	1130006852058761881	0 22 28 52 96 130 150 162 196 208 228 262 306 330 336 358	1468826950142
TPT(14)	1130006910791432831	0 2 48 50 78 80 120 122 258 260 276 278 306 308	1527559621092
SPT(16)	1130007384184405393	0 10 28 30 64 88 118 148 156 186 216 240 274 276 294 304	2000952593654