Prime p₀= 1012100888895124109 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 100 2 94 2 28 2 82 2 64 2 58 2 (?)
a_n: 0 2 102 104 198 200 228 230 312 314 378 380 438 440
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: 440
Found by: stoneageman
db: batch=76, k=14, 100 94 28 82 64 58

SPT(16)	1012099671782772367	0 6 12 16 64 100 120 130 156 166 186 222 270 274 280 286	-1217112351742
STPT(10)	1012099791530457599	0 2 12 14 30 32 48 50 60 62	-1097364666510
SPT(16)	1012099822373783387	0 12 26 30 32 72 80 96 116 132 140 180 182 186 200 212	-1066521340722
SPT(16)	1012099956831302197	0 36 66 82 102 150 166 172 210 216 232 280 300 316 346 382	-932063821912
TPT(14)	1012100819055888827	0 2 72 74 114 116 144 146 180 182 192 194 210 212	-69839235282
TPT(14)	1012100837384460779	0 2 48 50 72 74 90 92 102 104 132 134 168 170	-51510663330
STPT(10)	1012101294465431591	0 2 36 38 78 80 120 122 156 158	405570307482
TPT(14)	1012101544745757251	0 2 60 62 78 80 90 92 186 188 198 200 240 242	655850633142
SPT(16)	1012101573269179597	0 100 112 114 130 144 154 172 234 252 262 276 292 294 306 406	684374055488
STPT(10)	1012101600712508939	0 2 42 44 90 92 138 140 180 182	711817384830
SPT(18)	1012102112447278651	0 58 66 78 82 88 142 156 178 240 262 276 330 336 340 352 360 418	1223552154542