Prime p₀= 3016115101045580291 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 10 2 10 2 4 2 (?)
a_n: 0 2 6 8 18 20 30 32 36 38
All 10 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 38
Found by: ginga
db: batch=82, k=10, 2 4 2 10 2

TPT(14)	3016113253454058617	0 2 30 32 60 62 144 146 252 254 270 272 312 314	-1847591521674
SPT(16)	3016113635385576703	0 54 66 70 106 120 124 126 148 150 154 168 204 208 220 274	-1465660003588
SPT(16)	3016113942869790811	0 10 46 76 90 102 130 132 136 138 166 178 192 222 258 268	-1158175789480
STPT(12)	3016114091000919509	0 2 42 44 150 152 282 284 390 392 432 434	-1010044660782
SPT(16)	3016114430207234999	0 12 14 44 90 152 170 174 188 192 210 272 318 348 350 362	-670838345292
SPT(16)	3016114730086145827	0 10 66 76 90 130 184 210 226 252 306 346 360 370 426 436	-370959434464
SPT(16)	3016115107133409917	0 6 20 42 56 86 116 206 216 306 336 366 380 402 416 422	6087829626
STPT(10)	3016115181582943199	0 2 12 14 90 92 168 170 180 182	80537362908
SPT(16)	3016115285594992283	0 20 104 120 126 146 170 204 230 264 288 308 314 330 414 434	184549411992
SPT(16)	3016115690218021381	0 58 96 106 156 198 246 280 378 412 460 502 552 562 600 658	589172441090
STPT(10)	3016115791135486967	0 2 54 56 72 74 90 92 144 146	690089906676