Prime p₀= 1550457069450450881 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 34 2 28 2 28 2 28 2 10 2 (?)
a_n: 0 2 30 32 66 68 96 98 126 128 156 158 168 170
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: 170
Found by: crashtech
db: batch=78, k=14, 28 34 28 28 28 10

STPT(10)	1550455834896882647	0 2 24 26 42 44 60 62 84 86	-1234553568234
STPT(10)	1550455873306157327	0 2 42 44 72 74 102 104 144 146	-1196144293554
TPT(14)	1550455964484345551	0 2 6 8 48 50 66 68 96 98 120 122 150 152	-1104966105330
STPT(10)	1550456903834144651	0 2 36 38 78 80 120 122 156 158	-165616306230
TPT(14)	1550456948778975551	0 2 30 32 150 152 186 188 198 200 228 230 276 278	-120671475330
SPT(16)	1550456956980965987	0 6 30 72 92 104 120 140 156 176 192 204 224 266 290 296	-112469484894
STPT(10)	1550457472344664307	0 2 12 14 72 74 132 134 144 146	402894213426
SPT(16)	1550457813552227341	0 16 28 42 76 90 132 142 156 166 208 222 256 270 282 298	744101776460
SPT(16)	1550457945318605363	0 20 24 66 80 96 134 140 144 150 188 204 218 260 264 284	875868154482
SPT(16)	1550458148869773427	0 40 72 82 124 160 180 190 264 274 294 330 372 382 414 454	1079419322546
SPT(16)	1550458243791113537	0 60 96 116 150 192 236 240 266 270 314 356 390 410 446 506	1174340662656