Prime p₀= 3091401592497275567 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 10 2 46 2 106 2 58 2 22 2 (?)
a_n: 0 2 12 14 24 26 72 74 180 182 240 242 264 266
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: 266
Found by: L@MiR
db: batch=83, k=14, 10 10 46 106 58 22

SPT(16)	3091400318364148121	0 2 38 50 60 132 192 200 258 266 326 398 408 420 456 458	-1274133127446
STPT(10)	3091400870718471107	0 2 30 32 42 44 54 56 84 86	-721778804460
STPT(12)	3091401030274307459	0 2 78 80 90 92 120 122 132 134 210 212	-562222968108
SPT(16)	3091401112878723259	0 4 28 58 60 72 114 150 172 208 250 262 264 294 318 322	-479618552308
SPT(16)	3091401292642889903	0 6 18 20 54 98 210 234 260 284 396 440 474 476 488 494	-299854385664
STPT(10)	3091401410557515569	0 2 48 50 90 92 132 134 180 182	-181939759998
SPT(16)	3091401779404726421	0 8 72 110 152 200 260 266 282 288 348 396 438 476 540 548	186907450854
STPT(10)	3091401975890096411	0 2 6 8 48 50 90 92 96 98	383392820844
STPT(10)	3091401985663733237	0 2 12 14 42 44 72 74 84 86	393166457670
SPT(18)	3091402354032100637	0 6 50 62 90 96 162 170 182 294 306 314 380 386 414 426 470 476	761534825070
SPT(16)	3091402552600826953	0 4 10 48 58 60 114 118 126 130 184 186 196 234 240 244	960103551386