Prime p₀= 404875827293055119 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 28 2 34 2 100 2 10 2 (?)
a_n: 0 2 42 44 72 74 108 110 210 212 222 224
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: 224
Found by: Cruncher Pete
db: batch=70, k=12, 40 28 34 100 10

SPT(14)	404875680952680499	0 4 18 60 64 100 102 130 132 168 172 214 228 232	-146340374620
TPT(12)	404875686976754141	0 2 30 32 66 68 78 80 120 122 126 128	-140316300978
STPT(10)	404875732668040817	0 2 30 32 42 44 54 56 84 86	-94625014302
STPT(10)	404875781035040561	0 2 36 38 78 80 120 122 156 158	-46258014558
SPT(14)	404875796034981311	0 42 56 120 126 140 152 210 222 236 242 306 320 362	-31258073808
SPT(14)	404875807137858377	0 14 44 54 72 90 114 122 146 164 182 192 222 236	-20155196742
SPT(14)	404875863487242779	0 8 42 48 108 140 162 170 192 224 284 290 324 332	36194187660
SPT(14)	404875879419906049	0 78 100 102 112 114 130 162 178 180 190 192 214 292	52126850930
STPT(10)	404875891564309367	0 2 42 44 72 74 102 104 144 146	64271254248
SPT(14)	404875893716336827	0 12 22 42 46 64 72 94 102 120 124 144 154 166	66423281708
SPT(14)	404875899379525801	0 6 16 28 36 42 52 96 106 112 120 132 142 148	72086470682