Prime p₀= 797832478437942107 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 10 2 4 2 10 2 10 2 (?)
a_n: 0 2 12 14 24 26 30 32 42 44 54 56
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 56
Found by: scrap
db: batch=73, k=12, 2 10 2 10 2 4

SPT(16)	797830353805883549	0 32 74 90 104 110 120 134 180 194 204 210 224 240 282 314	-2124632058558
SPT(16)	797830504090391869	0 4 18 28 54 84 100 130 138 168 184 214 240 250 264 268	-1974347550238
SPT(16)	797830579751195083	0 36 48 64 70 108 114 136 168 190 196 234 240 256 268 304	-1898686747024
SPT(16)	797831994888708733	0 16 64 76 78 126 148 150 154 156 178 226 228 240 288 304	-483549233374
SPT(16)	797832110093540297	0 2 12 24 26 74 96 140 156 200 222 270 272 284 294 296	-368344401810
TPT(14)	797832478437942041	0 2 66 68 78 80 90 92 96 98 108 110 120 122	-66
STPT(10)	797832628413609071	0 2 6 8 48 50 90 92 96 98	149975666964
STPT(10)	797832803565667949	0 2 48 50 60 62 72 74 120 122	325127725842
STPT(10)	797832852612917489	0 2 18 20 30 32 42 44 60 62	374174975382
SPT(20)	797833092256371827	0 42 96 110 122 144 162 194 206 222 314 330 342 374 392 414 426 440 494 536	613818429720
STPT(10)	797833168044172187	0 2 42 44 72 74 102 104 144 146	689606230080