Prime p₀= 868201371046898321 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 94 2 10 2 70 2 28 2 28 2 34 2 (?)
a_n: 0 2 96 98 108 110 180 182 210 212 240 242 276 278
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: 278
Found by: [SG-2W]Kurzer
db: batch=73, k=14, 94 10 70 28 28 34

SPT(16)	868199718107050151	0 6 18 96 120 128 138 146 210 218 228 236 260 338 350 356	-1652939848170
STPT(10)	868199825906190077	0 2 24 26 42 44 60 62 84 86	-1545140708244
SPT(16)	868200061247858917	0 30 34 40 64 114 120 130 156 166 172 222 246 252 256 286	-1309799039404
SPT(16)	868200222432524341	0 12 72 76 118 136 138 166 192 220 222 240 282 286 346 358	-1148614373980
SPT(16)	868200868898834983	0 18 28 36 78 120 130 184 210 264 274 316 358 366 376 394	-502148063338
SPT(16)	868200963757130093	0 18 30 48 54 56 90 114 140 164 198 200 206 224 236 254	-407289768228
STPT(10)	868201585592079197	0 2 30 32 42 44 54 56 84 86	214545180876
STPT(10)	868202313134738669	0 2 42 44 90 92 138 140 180 182	942087840348
STPT(10)	868202371941906731	0 2 36 38 78 80 120 122 156 158	1000895008410
SPT(16)	868202459801506847	0 6 44 56 92 96 114 134 342 362 380 384 420 432 470 476	1088754608526
STPT(10)	868202509242161879	0 2 78 80 120 122 162 164 240 242	1138195263558