Prime p₀= 378643993439288741 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 106 2 28 2 160 2 34 2 10 2 (?)
a_n: 0 2 108 110 138 140 300 302 336 338 348 350
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: 350
Found by: Cruncher Pete
db: batch=70, k=12, 106 28 160 34 10

SPT(14)	378643932408269713	0 16 48 54 70 96 138 196 238 264 280 286 318 334	-61031019028
STPT(10)	378643941436243667	0 2 30 32 60 62 90 92 120 122	-52003045074
SPT(14)	378643941667254391	0 16 42 66 112 142 156 256 270 300 346 370 396 412	-51772034350
TPT(12)	378643944099327461	0 2 18 20 78 80 168 170 240 242 300 302	-49339961280
SPT(14)	378643971679882759	0 22 30 70 90 102 114 130 142 154 174 214 222 244	-21759405982
SPT(16)	378643975296170191	0 12 70 76 88 136 168 186 202 220 252 300 312 318 376 388	-18143118550
TPT(12)	378644014870062041	0 2 18 20 36 38 48 50 60 62 126 128	21430773300
SPT(14)	378644033991284077	0 4 70 84 144 156 162 184 190 202 262 276 342 346	40551995336
SPT(14)	378644034127486553	0 6 26 48 56 90 98 108 116 150 158 180 200 206	40688197812
SPT(14)	378644044915199071	0 16 30 42 112 136 142 150 156 180 250 262 276 292	51475910330
SPT(14)	378644047973887691	0 30 56 62 72 86 150 272 336 350 360 366 392 422	54534598950