Prime p₀= 2569535361959196731 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 166 2 88 2 10 2 124 2 112 2 28 2 (?)
a_n: 0 2 168 170 258 260 270 272 396 398 510 512 540 542
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: 542
Found by: JayPi
db: batch=82, k=14, 166 88 10 124 112 28

STPT(10)	2569534254607638221	0 2 36 38 78 80 120 122 156 158	-1107351558510
SPT(16)	2569534268478389543	0 6 48 86 104 216 218 224 240 246 248 360 378 416 458 464	-1093480807188
SPT(16)	2569534467918043481	0 8 30 48 56 78 116 120 338 342 380 402 410 428 450 458	-894041153250
SPT(16)	2569534634096587519	0 60 102 118 168 180 192 214 258 280 292 304 354 370 412 472	-727862609212
STPT(10)	2569535097639733997	0 2 42 44 72 74 102 104 144 146	-264319462734
STPT(10)	2569535167711075181	0 2 36 38 78 80 120 122 156 158	-194248121550
SPT(16)	2569535534130715291	0 10 142 148 162 186 318 336 382 400 532 556 570 576 708 718	172171518560
SPT(16)	2569535660888167693	0 16 28 30 54 66 100 138 166 204 238 250 274 276 288 304	298928970962
STPT(10)	2569535664128684309	0 2 42 44 60 62 78 80 120 122	302169487578
STPT(10)	2569535670191853227	0 2 12 14 72 74 132 134 144 146	308232656496
SPT(16)	2569535762259193333	0 58 106 114 124 160 166 180 184 198 204 240 250 258 306 364	400299996602