Prime p₀= 945588431984426537 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 40 2 64 2 10 2 46 2 (?)
a_n: 0 2 30 32 72 74 114 116 180 182 192 194 240 242
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: 242
Found by: HenkM
db: batch=76, k=14, 28 40 40 64 10 46

SPT(16)	945586656541211483	0 30 50 68 78 120 128 170 234 276 284 326 336 354 374 404	-1775443215054
SPT(16)	945586703630511359	0 8 14 48 74 110 120 140 222 242 252 288 314 348 354 362	-1728353915178
SPT(16)	945587336725161397	0 10 36 64 66 150 154 172 204 222 226 310 312 340 366 376	-1095259265140
STPT(10)	945587369570072531	0 2 30 32 78 80 126 128 156 158	-1062414354006
STPT(10)	945587988178055309	0 2 42 44 90 92 138 140 180 182	-443806371228
SPT(16)	945588034394867891	0 20 26 42 62 128 140 152 186 198 210 276 296 312 318 338	-397589558646
SPT(20)	945588472940662457	0 36 44 60 62 90 92 102 144 162 194 212 254 264 266 294 296 312 320 356	40956235920
SPT(16)	945588665627980597	0 4 10 12 54 66 70 100 126 156 160 172 214 216 222 226	233643554060
SPT(16)	945588701922781547	0 2 24 44 50 66 72 116 120 164 170 186 192 212 234 236	269938355010
STPT(10)	945588954381014789	0 2 18 20 30 32 42 44 60 62	522396588252
STPT(10)	945589548431720417	0 2 30 32 42 44 54 56 84 86	1116447293880