Prime p₀= 867743244011677877 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 88 2 64 2 178 2 70 2 10 2 (?)
a_n: 0 2 84 86 174 176 240 242 420 422 492 494 504 506
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: 506
Found by: [AF>Amis des Lapins] Ceclo
db: batch=73, k=14, 82 88 64 178 70 10

SPT(16)	867741613426393339	0 28 30 34 58 64 90 154 168 232 258 264 288 292 294 322	-1630585284538
SPT(16)	867741744745540697	0 14 30 44 54 74 84 86 114 116 126 146 156 170 186 200	-1499266137180
STPT(10)	867741855629711057	0 2 30 32 72 74 114 116 144 146	-1388381966820
STPT(12)	867742384445363639	0 2 18 20 42 44 78 80 102 104 120 122	-859566314238
SPT(16)	867742705998565027	0 22 30 36 46 70 96 102 124 130 156 180 190 196 204 226	-538013112850
SPT(16)	867742896870172877	0 30 42 72 92 110 134 144 152 162 186 204 224 254 266 296	-347141505000
STPT(12)	867743342729349131	0 2 66 68 108 110 138 140 180 182 246 248	98717671254
STPT(12)	867743363257834097	0 2 12 14 24 26 60 62 72 74 84 86	119246156220
STPT(10)	867743528729054009	0 2 48 50 90 92 132 134 180 182	284717376132
TPT(14)	867743597044737947	0 2 72 74 240 242 252 254 294 296 312 314 354 356	353033060070
SPT(16)	867743620521189047	0 6 20 72 86 122 150 174 182 206 234 270 284 336 350 356	376509511170