Prime p₀= 2027258368621041299 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 100 2 16 2 10 2 34 2 82 2 76 2 (?)
a_n: 0 2 102 104 120 122 132 134 168 170 252 254 330 332
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: 332
Found by: vaughan
db: batch=80, k=14, 100 16 10 34 82 76

SPT(16)	2027257405065713581	0 18 76 78 106 120 132 148 150 166 178 192 220 222 280 298	-963555327718
SPT(16)	2027257449072287137	0 10 12 16 46 54 66 70 156 160 172 180 210 214 216 226	-919548754162
STPT(10)	2027257523471823791	0 2 30 32 78 80 126 128 156 158	-845149217508
SPT(16)	2027257634489244457	0 40 46 70 76 82 102 112 114 124 144 150 156 180 186 226	-734131796842
STPT(10)	2027257906579460297	0 2 12 14 42 44 72 74 84 86	-462041581002
SPT(16)	2027258056511724313	0 6 34 36 114 124 160 216 238 294 330 340 418 420 448 454	-312109316986
STPT(10)	2027258554575095729	0 2 18 20 30 32 42 44 60 62	185954054430
STPT(10)	2027259090417336071	0 2 6 8 18 20 30 32 36 38	721796294772
SPT(16)	2027259236098685623	0 40 46 138 150 154 160 196 198 234 240 244 256 348 354 394	867477644324
STPT(10)	2027259564159504089	0 2 18 20 30 32 42 44 60 62	1195538462790
TPT(14)	2027259601078115561	0 2 48 50 108 110 210 212 216 218 276 278 306 308	1232457074262