Prime p₀= 223391923687790519 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 10 2 28 2 106 2 16 2 22 2 (?)
a_n: 0 2 60 62 72 74 102 104 210 212 228 230 252 254
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: 254
Found by: Alnitak2019
db: batch=69, k=14, 58 10 28 106 16 22

SPT(14)	223391843239394923	0 18 34 46 78 108 168 196 256 286 318 330 346 364	-80448395596
SPT(14)	223391868780658957	0 54 60 84 124 142 162 172 192 210 250 274 280 334	-54907131562
SPT(14)	223391893569990107	0 26 36 72 96 110 144 152 186 200 224 260 270 296	-30117800412
SPT(14)	223391912349138979	0 24 78 94 102 150 160 162 172 220 228 244 298 322	-11338651540
TPT(12)	223391912935895477	0 2 42 44 54 56 72 74 180 182 210 212	-10751895042
TPT(12)	223391923369497107	0 2 24 26 84 86 210 212 252 254 264 266	-318293412
SPT(14)	223391932074349433	0 38 44 90 104 108 174 290 356 360 374 420 426 464	8386558914
SPT(14)	223391932973840159	0 2 12 72 110 114 132 140 158 162 200 260 270 272	9286049640
SPT(14)	223391934119658253	0 24 66 78 118 130 136 288 294 306 346 358 400 424	10431867734
SPT(14)	223391936072536303	0 64 70 90 160 204 210 220 226 270 340 360 366 430	12384745784
SPT(14)	223391942722565231	0 2 30 42 60 62 98 102 138 140 158 170 198 200	19034774712