Prime p₀= 2015401040417330789 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 58 2 40 2 166 2 40 2 10 2 (?)
a_n: 0 2 108 110 168 170 210 212 378 380 420 422 432 434
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: 434
Found by: Chooka
db: batch=80, k=14, 106 58 40 166 40 10

SPT(16)	2015399129920371163	0 90 100 124 138 154 234 238 330 334 414 430 444 468 478 568	-1910496959626
TPT(14)	2015399649458195927	0 2 90 92 132 134 174 176 234 236 342 344 372 374	-1390959134862
SPT(13)	2015399695485318193	0 36 60 78 126 168 198 228 270 318 336 360 396	-1344932012596
SPT(16)	2015400363396506071	0 12 66 96 100 126 192 198 250 256 322 348 352 382 436 448	-677020824718
STPT(10)	2015400944459112809	0 2 18 20 30 32 42 44 60 62	-95958217980
SPT(16)	2015400970929731141	0 26 78 108 116 150 180 182 246 248 278 312 320 350 402 428	-69487599648
SPT(16)	2015401097602443211	0 6 12 22 30 40 126 156 166 196 282 292 300 310 316 322	57185112422
SPT(16)	2015401107387075337	0 4 12 24 30 52 54 90 94 130 132 154 160 172 180 184	66969744548
STPT(10)	2015401593278311541	0 2 30 32 120 122 210 212 240 242	552860980752
SPT(16)	2015401978345282103	0 14 44 48 78 84 110 126 218 234 260 266 296 300 330 344	937927951314
SPT(16)	2015402218614144589	0 34 78 82 144 180 264 294 298 328 412 448 510 514 558 592	1178196813800