Prime p₀= 2361683279281050677 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 16 2 52 2 148 2 16 2 10 2 (?)
a_n: 0 2 12 14 30 32 84 86 234 236 252 254 264 266
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: 266
Found by: Landjunge
db: batch=81, k=14, 10 16 52 148 16 10

SPT(16)	2361682059650391581	0 68 120 122 132 152 162 168 230 236 246 266 276 278 330 398	-1219630659096
SPT(16)	2361682119791967611	0 8 30 42 80 126 156 176 192 212 242 288 326 338 360 368	-1159489083066
STPT(10)	2361682699365015071	0 2 48 50 108 110 168 170 216 218	-579916035606
SPT(16)	2361682778727435929	0 44 50 72 138 192 258 348 374 464 530 584 650 672 678 722	-500553614748
SPT(16)	2361683134053224851	0 42 48 52 88 90 112 132 148 168 190 192 228 232 238 280	-145227825826
STPT(10)	2361683206263547181	0 2 30 32 120 122 210 212 240 242	-73017503496
TPT(14)	2361683328814351877	0 2 252 254 324 326 360 362 390 392 420 422 474 476	49533301200
TPT(14)	2361683424878135051	0 2 36 38 108 110 210 212 306 308 336 338 390 392	145597084374
SPT(16)	2361684228069332473	0 4 90 118 154 180 198 240 268 310 328 354 390 418 504 508	948788281796
SPT(16)	2361685145314660939	0 34 60 64 132 144 210 222 400 412 478 490 558 562 588 622	1866033610262
STPT(10)	2361685403153685491	0 2 36 38 78 80 120 122 156 158	2123872634814