Prime p₀= 1282474997730150821 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 58 2 40 2 34 2 28 2 22 2 (?)
a_n: 0 2 18 20 78 80 120 122 156 158 186 188 210 212
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: 212
Found by: Cruncher Pete
db: batch=77, k=14, 16 58 40 34 28 22

TPT(14)	1282473730131672599	0 2 42 44 48 50 78 80 120 122 222 224 252 254	-1267598478222
STPT(10)	1282473989927717339	0 2 18 20 30 32 42 44 60 62	-1007802433482
TPT(14)	1282474102365453089	0 2 30 32 42 44 108 110 162 164 210 212 240 242	-895364697732
SPT(16)	1282474234029208313	0 36 38 44 80 84 104 114 140 150 170 174 210 216 218 254	-763700942508
SPT(16)	1282474895718732029	0 84 90 122 132 140 150 152 270 272 282 290 300 332 338 422	-102011418792
SPT(16)	1282474968735631159	0 42 52 60 82 112 118 180 250 312 318 348 370 378 388 430	-28994519662
STPT(10)	1282475150382366761	0 2 6 8 18 20 30 32 36 38	152652215940
STPT(10)	1282475227262383211	0 2 30 32 78 80 126 128 156 158	229532232390
TPT(14)	1282475252469347897	0 2 42 44 114 116 120 122 132 134 204 206 210 212	254739197076
SPT(16)	1282475421495176801	0 8 62 92 98 158 168 236 252 320 330 390 396 426 480 488	423765025980
SPT(16)	1282475442298683251	0 42 86 92 128 132 138 152 276 290 296 300 336 342 386 428	444568532430