Prime p₀= 2589574368753764471 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 118 2 34 2 28 2 112 2 64 2 40 2 (?)
a_n: 0 2 120 122 156 158 186 188 300 302 366 368 408 410
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: 410
Found by: JayPi
db: batch=82, k=14, 118 34 28 112 64 40

SPT(16)	2589572415489188009	0 14 18 74 80 132 140 170 312 342 350 402 408 464 468 482	-1953264576462
TPT(14)	2589572942968280849	0 2 60 62 138 140 192 194 270 272 318 320 348 350	-1425785483622
STPT(10)	2589573286081452941	0 2 6 8 48 50 90 92 96 98	-1082672311530
SPT(16)	2589573861366060589	0 30 34 40 52 54 60 70 114 124 130 132 144 150 154 184	-507387703882
STPT(10)	2589573972483075167	0 2 42 44 72 74 102 104 144 146	-396270689304
TPT(14)	2589574228582797809	0 2 12 14 132 134 138 140 150 152 288 290 300 302	-140170966662
TPT(14)	2589574444107243161	0 2 30 32 60 62 156 158 228 230 258 260 270 272	75353478690
SPT(16)	2589574488066587851	0 40 46 82 118 120 168 172 456 460 508 510 546 582 588 628	119312823380
STPT(12)	2589575065637782637	0 2 30 32 42 44 72 74 84 86 114 116	696884018166
SPT(16)	2589575494783094813	0 48 56 80 156 168 270 290 294 314 416 428 504 528 536 584	1126029330342
SPT(16)	2589575617026539329	0 34 60 70 82 84 112 130 174 192 220 222 234 244 270 304	1248272774858