Prime p₀= 2807598131308946009 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 100 2 46 2 16 2 22 2 16 2 10 2 (?)
a_n: 0 2 102 104 150 152 168 170 192 194 210 212 222 224
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: 224
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 100 46 16 22 16 10

SPT(16)	2807597145602067439	0 4 18 60 84 118 124 148 150 174 180 214 238 280 294 298	-985706878570
SPT(16)	2807597368786451071	0 22 28 42 52 88 120 136 162 178 210 246 256 270 276 298	-762522494938
SPT(16)	2807597373150959453	0 30 36 56 110 116 126 140 180 194 204 210 264 284 290 320	-758157986556
SPT(16)	2807597614666187947	0 22 24 142 174 262 270 274 282 286 294 382 414 532 534 556	-516642758062
STPT(10)	2807597651959265447	0 2 60 62 102 104 144 146 204 206	-479349680562
SPT(16)	2807597809472421871	0 162 168 190 198 246 252 306 352 406 412 460 468 490 496 658	-321836524138
SPT(16)	2807598210159704893	0 10 28 54 70 78 88 94 114 120 130 138 154 180 198 208	78850758884
SPT(16)	2807598515967876331	0 10 112 120 148 150 180 210 250 280 310 312 340 348 450 460	384658930322
SPT(16)	2807598836622097157	0 12 50 90 122 162 236 254 342 360 434 474 506 546 584 596	705313151148
STPT(10)	2807598838611339737	0 2 30 32 42 44 54 56 84 86	707302393728
STPT(10)	2807599220250239417	0 2 30 32 60 62 90 92 120 122	1088941293408