Prime p₀= 1411665264815806667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 16 2 58 2 40 2 10 2 34 2 (?)
a_n: 0 2 42 44 60 62 120 122 162 164 174 176 210 212
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: MarkRBright
db: batch=78, k=14, 40 16 58 40 10 34

SPT(16)	1411663679035384069	0 40 42 64 72 88 138 142 150 154 204 220 228 250 252 292	-1585780422598
SPT(16)	1411664291593637351	0 48 92 132 156 186 212 252 386 426 452 482 506 546 590 638	-973222169316
SPT(16)	1411664851178001239	0 14 18 30 54 74 108 150 158 200 234 254 278 290 294 308	-413637805428
SPT(16)	1411664902761572273	0 8 20 36 90 138 146 170 174 198 206 254 308 324 336 344	-362054234394
SPT(16)	1411665002048864093	0 6 44 56 90 114 156 194 270 308 350 374 408 420 458 464	-262766942574
SPT(16)	1411665008838345529	0 4 10 30 48 60 120 228 244 352 412 424 442 462 468 472	-255977461138
STPT(10)	1411665387608714219	0 2 42 44 60 62 78 80 120 122	122792907552
STPT(10)	1411665407142352487	0 2 30 32 72 74 114 116 144 146	142326545820
STPT(10)	1411665691539174737	0 2 30 32 120 122 210 212 240 242	426723368070
TPT(14)	1411665709149385901	0 2 360 362 378 380 390 392 408 410 540 542 576 578	444333579234
SPT(16)	1411665897824595997	0 22 24 70 114 154 184 190 204 210 240 280 324 370 372 394	633008789330