Prime p₀= 2234573484750751757 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 10 2 28 2 28 2 16 2 (?)
a_n: 0 2 30 32 42 44 54 56 84 86 114 116 132 134
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: 134
Found by: Penguin
db: batch=81, k=14, 28 10 10 28 28 16

SPT(18)	2234571139106467907	0 12 20 42 74 102 110 126 132 224 230 246 254 282 314 336 344 356	-2345644283850
SPT(16)	2234571179761144121	0 8 98 128 156 182 218 248 300 330 366 392 420 450 540 548	-2304989607636
STPT(12)	2234571386961558527	0 2 42 44 84 86 150 152 192 194 234 236	-2097789193230
SPT(16)	2234571688946202769	0 10 22 60 64 88 102 154 168 220 234 258 262 300 312 322	-1795804548988
SPT(16)	2234572034449164041	0 36 38 66 86 140 150 158 168 176 186 240 260 288 290 326	-1450301587716
STPT(10)	2234572243139841359	0 2 18 20 30 32 42 44 60 62	-1241610910398
STPT(10)	2234573484750751757	0 2 30 32 42 44 54 56 84 86	0
SPT(16)	2234573871377635019	0 8 24 38 42 102 108 134 168 194 200 260 264 278 294 302	386626883262
SPT(16)	2234573969672272897	0 54 82 106 120 132 160 180 226 246 274 286 300 324 352 406	484921521140
STPT(10)	2234574677260408697	0 2 42 44 132 134 222 224 264 266	1192509656940
STPT(10)	2234575103694484247	0 2 54 56 132 134 210 212 264 266	1618943732490