Prime p₀= 1124923119373760921 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 28 2 64 2 28 2 28 2 (?)
a_n: 0 2 30 32 60 62 126 128 156 158 186 188
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: 188
Found by: crashtech
db: batch=76, k=12, 2 28 2 28 2 64

STPT(10)	1124922288543683657	0 2 30 32 42 44 54 56 84 86	-830830077264
STPT(10)	1124922468102391487	0 2 12 14 42 44 72 74 84 86	-651271369434
SPT(18)	1124922633152749693	0 10 40 70 78 100 108 120 126 190 196 208 216 238 246 276 306 316	-486221011228
SPT(16)	1124922687581692591	0 36 40 42 48 72 96 106 132 142 166 190 196 198 202 238	-431792068330
SPT(16)	1124922850012588021	0 22 28 30 126 136 142 150 238 246 252 262 358 360 366 388	-269361172900
SPT(16)	1124923046734679917	0 40 46 106 130 156 160 190 222 252 256 282 306 366 372 412	-72639081004
SPT(16)	1124923261730431349	0 14 50 60 72 90 110 132 140 162 182 200 212 222 258 272	142356670428
SPT(16)	1124923314170346659	0 8 14 20 44 62 78 104 108 134 150 168 192 198 204 212	194796585738
TPT(14)	1124923609429431311	0 2 36 38 66 68 90 92 126 128 216 218 360 362	490055670390
TPT(14)	1124923667951735651	0 2 60 62 138 140 150 152 156 158 180 182 348 350	548577974730
SPT(16)	1124923812694478471	0 6 26 50 72 90 110 120 182 192 212 230 252 276 296 302	693320717550