Prime p₀= 2596626438827064431 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 94 2 10 2 28 2 16 2 22 2 (?)
a_n: 0 2 30 32 126 128 138 140 168 170 186 188 210 212
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: [SG-FC] hl
db: batch=82, k=14, 28 94 10 28 16 22

SPT(16)	2596625371503963857	0 2 122 134 182 200 204 266 390 452 456 474 522 534 654 656	-1067323100574
STPT(10)	2596626160584252491	0 2 30 32 60 62 90 92 120 122	-278242811940
STPT(10)	2596626162899007059	0 2 18 20 30 32 42 44 60 62	-275928057372
STPT(10)	2596626187843707917	0 2 60 62 102 104 144 146 204 206	-250983356514
SPT(16)	2596626202692376837	0 16 112 132 136 156 264 292 294 322 430 450 454 474 570 586	-236134687594
SPT(16)	2596626320895335101	0 10 16 36 42 60 66 88 90 112 118 136 142 162 168 178	-117931729330
SPT(16)	2596626525491781577	0 22 36 40 72 90 156 196 216 256 322 340 372 376 390 412	86664717146
STPT(10)	2596627338159849089	0 2 18 20 30 32 42 44 60 62	899332784658
SPT(16)	2596628024857064543	0 50 60 114 134 170 204 210 218 224 258 294 314 368 378 428	1586030000112
SPT(16)	2596628122062944219	0 8 20 48 68 92 98 108 122 132 138 162 182 210 222 230	1683235879788
SPT(16)	2596628205997778089	0 130 168 208 210 258 300 348 364 412 454 502 504 544 582 712	1767170713658