Prime p₀= 2788830146800403087 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 22 2 58 2 58 2 46 2 46 2 (?)
a_n: 0 2 30 32 54 56 114 116 174 176 222 224 270 272
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: JohnMD
db: batch=82, k=14, 28 22 58 58 46 46

SPT(16)	2788828793265108821	0 6 8 62 78 80 90 96 122 128 138 140 156 210 212 218	-1353535294266
STPT(10)	2788829221008128897	0 2 30 32 42 44 54 56 84 86	-925792274190
STPT(10)	2788829689499337299	0 2 12 14 30 32 48 50 60 62	-457301065788
STPT(10)	2788829997277065347	0 2 12 14 72 74 132 134 144 146	-149523337740
SPT(16)	2788830066352035799	0 64 70 108 114 142 148 172 210 234 240 268 274 312 318 382	-80448367288
TPT(14)	2788830068596296299	0 2 78 80 108 110 180 182 222 224 282 284 420 422	-78204106788
SPT(22)	2788830167006696389	0 48 54 64 84 108 114 148 154 244 280 288 324 414 420 454 460 484 504 514 520 568	20206293302
SPT(16)	2788830412877930789	0 8 42 60 92 104 128 144 158 174 198 210 242 260 294 302	266077527702
SPT(16)	2788830599545818473	0 38 48 66 78 104 116 128 246 258 270 296 308 326 336 374	452745415386
SPT(16)	2788830763015007077	0 42 54 70 76 162 226 262 264 300 364 450 456 472 484 526	616214603990
STPT(10)	2788831236166651901	0 2 36 38 78 80 120 122 156 158	1089366248814