Prime p₀= 1971725076012032021 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 10 2 220 2 28 2 28 2 34 2 (?)
a_n: 0 2 36 38 48 50 270 272 300 302 330 332 366 368
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: 368
Found by: Cruncher Pete
db: batch=80, k=14, 34 10 220 28 28 34

SPT(16)	1971723987524462863	0 48 70 76 96 118 126 180 256 310 318 340 360 366 388 436	-1088487569158
SPT(16)	1971724158505485751	0 90 126 138 156 160 196 198 208 210 246 250 268 280 316 406	-917506546270
STPT(10)	1971724614949650257	0 2 12 14 72 74 132 134 144 146	-461062381764
SPT(16)	1971724830962093059	0 4 58 90 102 108 112 172 180 240 244 250 262 294 348 352	-245049938962
SPT(16)	1971724903819538117	0 26 96 144 150 152 164 194 222 252 264 266 272 320 390 416	-172192493904
SPT(16)	1971724996720149479	0 20 42 48 90 102 128 230 282 384 410 422 464 470 492 512	-79291882542
STPT(10)	1971725881168204547	0 2 12 14 42 44 72 74 84 86	805156172526
STPT(10)	1971725920686434579	0 2 42 44 60 62 78 80 120 122	844674402558
SPT(16)	1971726099377732353	0 6 24 36 40 66 90 106 138 154 178 204 208 220 238 244	1023365700332
STPT(10)	1971726298184463641	0 2 6 8 18 20 30 32 36 38	1222172431620
SPT(16)	1971726664676628779	0 2 24 90 104 134 150 164 300 314 330 360 374 440 462 464	1588664596758