Prime p₀= 1126495880992278497 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 82 2 4 2 40 2 16 2 10 2 (?)
a_n: 0 2 30 32 114 116 120 122 162 164 180 182 192 194
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: 194
Found by: crashtech
db: batch=76, k=14, 28 82 4 40 16 10

STPT(10)	1126495196416680017	0 2 54 56 72 74 90 92 144 146	-684575598480
STPT(10)	1126495402411345037	0 2 30 32 42 44 54 56 84 86	-478580933460
SPT(16)	1126495549280516447	0 14 30 44 92 114 140 152 162 174 200 222 270 284 300 314	-331711762050
SPT(16)	1126495679241830221	0 58 70 106 120 126 130 136 162 168 172 178 192 228 240 298	-201750448276
STPT(10)	1126495765818711329	0 2 18 20 30 32 42 44 60 62	-115173567168
SPT(16)	1126495865286745799	0 18 20 30 42 68 72 84 158 170 174 200 212 222 224 242	-15705532698
STPT(10)	1126495926695296457	0 2 24 26 42 44 60 62 84 86	45703017960
STPT(10)	1126496006560224101	0 2 6 8 48 50 90 92 96 98	125567945604
SPT(16)	1126496014850576683	0 34 106 108 120 136 148 174 190 216 228 244 256 258 330 364	133858298186
STPT(10)	1126496133145218497	0 2 54 56 132 134 210 212 264 266	252152940000
SPT(16)	1126496971172924489	0 8 12 14 20 48 78 110 132 164 194 222 228 230 234 242	1090180645992