Prime p₀= 2038965305184358721 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 118 2 34 2 28 2 10 2 10 2 46 2 (?)
a_n: 0 2 120 122 156 158 186 188 198 200 210 212 258 260
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: 260
Found by: Landjunge
db: batch=80, k=14, 118 34 28 10 10 46

SPT(18)	2038964194661890201	0 18 52 76 88 102 112 118 132 136 150 156 166 180 192 216 250 268	-1110522468520
STPT(10)	2038964241386617547	0 2 30 32 60 62 90 92 120 122	-1063797741174
SPT(16)	2038964267714920643	0 54 56 126 140 164 168 174 230 236 240 264 278 348 350 404	-1037469438078
SPT(16)	2038964281567664947	0 4 84 132 202 222 240 300 334 394 412 432 502 550 630 634	-1023616693774
SPT(16)	2038964735656806949	0 54 60 82 84 102 112 124 150 162 172 190 192 214 220 274	-569527551772
SPT(16)	2038964774742829117	0 72 84 126 186 196 262 276 280 294 360 370 430 472 484 556	-530441529604
SPT(16)	2038966393795018211	0 6 42 66 96 102 122 150 188 216 236 242 272 296 332 338	1088610659490
SPT(16)	2038966891547606171	0 26 126 132 152 162 170 182 216 228 236 246 266 272 372 398	1586363247450
SPT(16)	2038966896924442747	0 16 54 82 126 160 216 286 330 400 456 490 534 562 600 616	1591740084026
STPT(10)	2038966954599916181	0 2 36 38 78 80 120 122 156 158	1649415557460
SPT(16)	2038966989654412943	0 6 14 20 24 48 56 90 164 198 206 230 234 240 248 254	1684470054222