Prime p₀= 1123466222673836441 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 16 2 40 2 148 2 16 2 22 2 (?)
a_n: 0 2 78 80 96 98 138 140 288 290 306 308 330 332
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: 332
Found by: crashtech
db: batch=76, k=14, 76 16 40 148 16 22

SPT(16)	1123465778022726311	0 6 20 56 66 96 122 132 140 150 176 206 216 252 266 272	-444651110130
TPT(14)	1123465823181556847	0 2 24 26 42 44 150 152 180 182 222 224 234 236	-399492279594
STPT(10)	1123465834634060369	0 2 48 50 90 92 132 134 180 182	-388039776072
SPT(16)	1123465977719070109	0 22 34 60 70 82 102 112 312 322 342 354 364 390 402 424	-244954766332
STPT(10)	1123466023223308157	0 2 30 32 42 44 54 56 84 86	-199450528284
SPT(16)	1123466053863449927	0 30 42 66 72 86 102 134 402 434 450 464 470 494 506 536	-168810386514
SPT(16)	1123466328891369899	0 14 38 42 44 78 80 104 108 132 134 168 170 174 198 212	106217533458
SPT(20)	1123466351612125483	0 4 6 34 46 58 70 78 84 130 144 190 196 204 216 228 240 268 270 274	128938289042
STPT(10)	1123466527291881317	0 2 30 32 42 44 54 56 84 86	304618044876
STPT(10)	1123466949706987181	0 2 6 8 18 20 30 32 36 38	727033150740
SPT(16)	1123467122785290071	0 8 18 20 26 32 62 66 92 96 126 132 138 140 150 158	900111453630