Prime p₀= 2556565881579595799 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 94 2 40 2 28 2 10 2 46 2 (?)
a_n: 0 2 42 44 138 140 180 182 210 212 222 224 270 272
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: 272
Found by: JayPi
db: batch=82, k=14, 40 94 40 28 10 46

SPT(16)	2556564740296420187	0 26 32 42 132 162 222 234 302 314 374 404 494 504 510 536	-1141283175612
STPT(10)	2556565233922818257	0 2 42 44 72 74 102 104 144 146	-647656777542
STPT(10)	2556565346707981517	0 2 30 32 42 44 54 56 84 86	-534871614282
TPT(14)	2556565366311002699	0 2 90 92 210 212 252 254 330 332 342 344 378 380	-515268593100
SPT(16)	2556565616227334713	0 18 40 94 138 144 154 156 178 180 190 196 240 294 316 334	-265352261086
STPT(10)	2556565751005432289	0 2 12 14 30 32 48 50 60 62	-130574163510
SPT(16)	2556565900394285071	0 6 18 40 48 90 168 216 292 340 418 460 468 490 502 508	18814689272
SPT(16)	2556565939757599831	0 12 42 46 112 136 150 180 202 232 246 270 336 340 370 382	58178004032
SPT(16)	2556566207523531421	0 52 66 82 100 102 106 142 150 186 190 192 210 226 240 292	325943935622
SPT(16)	2556566403666620117	0 2 6 12 56 66 80 90 146 156 170 180 224 230 234 236	522087024318
SPT(16)	2556566577208845623	0 30 38 86 126 134 140 164 210 234 240 248 288 336 344 374	695629249824