Prime p₀= 2362426487208097307 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 22 2 4 2 22 2 28 2 (?)
a_n: 0 2 30 32 54 56 60 62 84 86 114 116
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: 116
Found by: arkiss
db: batch=81, k=12, 2 28 2 22 2 4

SPT(16)	2362425024397337513	0 6 20 38 108 144 188 206 228 246 290 326 396 414 428 434	-1462810759794
STPT(10)	2362425294460199789	0 2 42 44 60 62 78 80 120 122	-1192747897518
STPT(10)	2362425775287061577	0 2 30 32 60 62 90 92 120 122	-711921035730
STPT(10)	2362425794484361811	0 2 6 8 18 20 30 32 36 38	-692723735496
SPT(16)	2362425825356491331	0 8 26 30 48 68 78 98 120 140 150 170 188 192 210 218	-661851605976
STPT(10)	2362425825754932797	0 2 30 32 72 74 114 116 144 146	-661453164510
STPT(10)	2362426559937163607	0 2 24 26 42 44 60 62 84 86	72729066300
SPT(16)	2362426685018052803	0 24 66 126 170 204 254 258 416 420 470 504 548 608 650 674	197809955496
STPT(10)	2362426934469446441	0 2 36 38 78 80 120 122 156 158	447261349134
SPT(16)	2362427299373619293	0 36 50 56 168 170 228 288 308 368 426 428 540 546 560 596	812165521986
SPT(16)	2362427340361427329	0 22 34 60 64 70 82 130 414 462 474 480 484 510 522 544	853153330022