Prime p₀= 4044829111017687359 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 34 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 78 80 108 110 120 122
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: 122
Found by: Alnitak2019
db: batch=84, k=12, 2 10 2 28 2 34

STPT(10)	4044828163529172989	0 2 12 14 30 32 48 50 60 62	-947488514370
SPT(16)	4044828333604944091	0 16 40 82 108 118 120 150 208 238 240 250 276 318 342 358	-777412743268
SPT(16)	4044828344177067649	0 12 82 88 90 112 138 222 250 334 360 382 384 390 460 472	-766840619710
TPT(14)	4044828756832784717	0 2 240 242 252 254 474 476 480 482 522 524 564 566	-354184902642
STPT(10)	4044828780312926729	0 2 12 14 30 32 48 50 60 62	-330704760630
TPT(14)	4044828849140192159	0 2 12 14 48 50 60 62 132 134 138 140 168 170	-261877495200
STPT(10)	4044829155941387237	0 2 54 56 72 74 90 92 144 146	44923699878
STPT(10)	4044829685182875599	0 2 48 50 90 92 132 134 180 182	574165188240
SPT(16)	4044831002488480951	0 10 48 96 102 136 178 222 286 330 372 406 412 460 498 508	1891470793592
TPT(14)	4044831315936710417	0 2 54 56 72 74 180 182 240 242 252 254 264 266	2204919023058
STPT(10)	4044831385202822897	0 2 42 44 72 74 102 104 144 146	2274185135538