Prime p₀= 2678509197364663121 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 64 2 58 2 28 2 28 2 40 2 (?)
a_n: 0 2 30 32 96 98 156 158 186 188 216 218 258 260
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: 260
Found by: JayPi
db: batch=82, k=14, 28 64 58 28 28 40

SPT(16)	2678507277597814879	0 28 54 90 112 144 154 160 192 198 208 240 262 298 324 352	-1919766848242
SPT(16)	2678507987780345243	0 26 48 74 164 180 186 230 264 308 314 330 420 446 468 494	-1209584317878
STPT(10)	2678508223753800377	0 2 30 32 60 62 90 92 120 122	-973610862744
SPT(16)	2678508436093333999	0 18 42 52 84 88 138 154 168 184 234 238 270 280 304 322	-761271329122
SPT(16)	2678508610710948901	0 12 28 36 40 42 48 72 166 190 196 198 202 210 226 238	-586653714220
STPT(10)	2678508732143734289	0 2 48 50 60 62 72 74 120 122	-465220928832
SPT(16)	2678509491461699563	0 6 84 156 198 288 324 336 358 370 406 496 538 610 688 694	294097036442
STPT(10)	2678509604935830899	0 2 48 50 60 62 72 74 120 122	407571167778
SPT(16)	2678509973142067511	0 20 42 66 72 126 150 156 182 188 212 266 272 296 318 338	775777404390
SPT(18)	2678510396470931431	0 10 36 40 52 76 142 156 192 376 412 426 492 516 528 532 558 568	1199106268310
SPT(16)	2678510652237069157	0 16 30 46 54 60 292 336 340 384 616 622 630 646 660 676	1454872406036