Prime p₀= 296058476665037111 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 16 2 28 2 76 2 112 2 16 2 (?)
a_n: 0 2 18 20 48 50 126 128 240 242 258 260
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: 260
Found by: vaughan
db: batch=69, k=12, 16 28 76 112 16

SPT(14)	296058341224343303	0 8 78 110 134 138 144 170 176 180 204 236 306 314	-135440693808
TPT(12)	296058389119305347	0 2 54 56 132 134 162 164 192 194 210 212	-87545731764
SPT(14)	296058429955538507	0 26 50 92 164 176 186 200 210 222 294 336 360 386	-46709498604
TPT(12)	296058449109431297	0 2 90 92 102 104 132 134 174 176 240 242	-27555605814
SPT(14)	296058454606018717	0 22 42 60 72 100 114 130 144 172 184 202 222 244	-22059018394
SPT(14)	296058470853335107	0 4 42 46 54 60 66 100 106 112 120 124 162 166	-5811702004
SPT(14)	296058479262510389	0 14 24 74 90 110 138 194 222 242 258 308 318 332	2597473278
SPT(14)	296058480717217313	0 18 90 144 146 198 236 258 296 348 350 404 476 494	4052180202
SPT(14)	296058482483880659	0 12 30 48 50 78 90 92 104 132 134 152 170 182	5818843548
TPT(12)	296058494627968901	0 2 6 8 36 38 48 50 90 92 138 140	17962931790
SPT(14)	296058510059466941	0 2 20 62 78 86 90 128 132 140 156 198 216 218	33394429830