Prime p₀= 2688055883752264469 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 40 2 88 2 76 2 88 2 118 2 (?)
a_n: 0 2 78 80 120 122 210 212 288 290 378 380 498 500
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: 500
Found by: JayPi
db: batch=82, k=14, 76 40 88 76 88 118

SPT(16)	2688054254914320007	0 30 36 42 52 72 136 144 322 330 394 414 424 430 436 466	-1628837944462
STPT(10)	2688054298239877067	0 2 54 56 72 74 90 92 144 146	-1585512387402
SPT(16)	2688054736422476077	0 4 54 220 222 282 306 312 334 340 364 424 426 592 642 646	-1147329788392
SPT(18)	2688054745298493521	0 98 158 170 192 230 242 252 290 318 356 366 378 416 438 450 510 608	-1138453770948
SPT(16)	2688055041261427457	0 12 14 26 92 180 204 210 266 272 296 384 450 462 464 476	-842490837012
SPT(16)	2688055542191599609	0 60 78 84 112 208 210 220 222 232 234 330 358 364 382 442	-341560664860
SPT(16)	2688055922883151147	0 6 10 34 52 90 94 192 214 312 316 354 372 396 400 406	39130886678
SPT(16)	2688055967049037573	0 84 88 114 130 148 184 190 198 204 240 258 274 300 304 388	83296773104
STPT(10)	2688056313791698901	0 2 6 8 18 20 30 32 36 38	430039434432
STPT(10)	2688056391559563839	0 2 42 44 90 92 138 140 180 182	507807299370
SPT(18)	2688056404404357031	0 30 40 48 66 90 100 178 180 196 198 276 286 310 328 336 346 376	520652092562