Prime p₀= 1056676034911587437 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 28 2 28 2 76 2 28 2 16 2 (?)
a_n: 0 2 84 86 114 116 144 146 222 224 252 254 270 272
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: 272
Found by: stoneageman
db: batch=76, k=14, 82 28 28 76 28 16

SPT(16)	1056675468498851413	0 70 90 106 108 130 136 150 154 168 174 196 198 214 234 304	-566412736024
STPT(10)	1056675535723215407	0 2 24 26 42 44 60 62 84 86	-499188372030
SPT(16)	1056675565062316597	0 16 24 34 40 52 72 82 84 94 114 126 132 142 150 166	-469849270840
SPT(16)	1056675630088506229	0 18 22 28 70 124 148 154 198 204 228 282 324 330 334 352	-404823081208
STPT(10)	1056675804390137609	0 2 18 20 30 32 42 44 60 62	-230521449828
SPT(16)	1056675819735734479	0 10 42 84 102 120 130 138 154 162 172 190 208 250 282 292	-215175852958
SPT(16)	1056676052618978879	0 42 54 72 80 110 174 182 222 230 294 324 332 350 362 404	17707391442
SPT(16)	1056676198133514793	0 16 24 46 60 66 90 94 126 130 154 160 174 196 204 220	163221927356
STPT(12)	1056676235701143479	0 2 102 104 132 134 168 170 198 200 300 302	200789556042
SPT(16)	1056676952846391161	0 18 32 38 116 140 152 182 186 216 228 252 330 336 350 368	917934803724
STPT(10)	1056677021077507757	0 2 12 14 72 74 132 134 144 146	986165920320