Prime p₀= 2851627213120933757 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 106 2 40 2 16 2 22 2 (?)
a_n: 0 2 30 32 72 74 180 182 222 224 240 242 264 266
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: JayPi
db: batch=82, k=14, 28 40 106 40 16 22

SPT(16)	2851624666239464993	0 26 66 108 146 150 170 180 224 234 254 258 296 338 378 404	-2546881468764
STPT(10)	2851625620258321889	0 2 12 14 90 92 168 170 180 182	-1592862611868
SPT(16)	2851625925966935281	0 10 42 52 112 138 142 156 202 216 220 246 306 316 348 358	-1287153998476
STPT(10)	2851626547087062011	0 2 36 38 78 80 120 122 156 158	-666033871746
SPT(16)	2851627049109884761	0 6 16 78 88 100 132 148 210 226 258 270 280 342 352 358	-164011048996
SPT(16)	2851627165281906169	0 42 48 54 72 100 132 148 174 190 222 250 268 274 280 322	-47839027588
SPT(16)	2851627249699552487	0 60 126 170 216 252 272 312 494 534 554 590 636 680 746 806	36578618730
SPT(16)	2851627453511482823	0 8 38 66 126 128 156 158 216 218 246 248 308 336 366 374	240390549066
STPT(10)	2851627473940578209	0 2 30 32 60 62 90 92 120 122	260819644452
SPT(16)	2851627525557569123	0 30 98 120 176 198 228 234 260 266 296 318 374 396 464 494	312436635366
SPT(16)	2851627567713893779	0 72 108 114 132 144 154 160 192 198 208 220 238 244 280 352	354592960022