Prime p₀= 2687675220599818367 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 28 2 58 2 28 2 148 2 28 2 (?)
a_n: 0 2 84 86 114 116 174 176 204 206 354 356 384 386
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: 386
Found by: RFGuy_KCCO
db: batch=82, k=14, 82 28 58 28 148 28

TPT(14)	2687673825270677921	0 2 18 20 30 32 66 68 96 98 138 140 186 188	-1395329140446
STPT(10)	2687674015721654117	0 2 12 14 72 74 132 134 144 146	-1204878164250
SPT(16)	2687674069244486321	0 18 48 80 138 146 186 200 216 230 270 278 336 368 398 416	-1151355332046
SPT(16)	2687674233183200039	0 32 42 80 84 104 182 234 308 360 438 458 462 500 510 542	-987416618328
STPT(10)	2687674665256452197	0 2 30 32 42 44 54 56 84 86	-555343366170
SPT(16)	2687674910421681017	0 32 50 74 96 116 164 186 200 222 270 290 312 336 354 386	-310178137350
STPT(10)	2687675250017906177	0 2 30 32 42 44 54 56 84 86	29418087810
SPT(16)	2687675299078945897	0 30 150 156 184 186 196 226 234 264 274 276 304 310 430 460	78479127530
SPT(16)	2687675462414356867	0 12 22 70 76 96 112 120 136 144 160 180 186 234 244 256	241814538500
SPT(16)	2687675753222276057	0 2 26 44 132 150 152 164 282 294 296 314 402 420 444 446	532622457690
SPT(20)	2687675921264404403	0 14 26 50 54 56 104 116 128 144 170 186 198 210 258 260 264 288 300 314	700664586036