Prime p₀= 2310378027901206829 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 34 8 46 14 22 48 8 22 8 48 22 14 46 8 34 (?)
a_n: 0 34 42 88 102 124 172 180 202 210 258 280 294 340 348 382
All 16 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 382
Found by: FritzB
db: batch=81, k=16, 34 8 46 14 22 48 8 22

SPT(16)	2310376300586716709	0 8 12 14 32 42 62 74 78 90 110 120 138 140 144 152	-1727314490120
TPT(14)	2310376314612086729	0 2 150 152 162 164 222 224 282 284 318 320 390 392	-1713289120100
STPT(10)	2310376622437324247	0 2 42 44 72 74 102 104 144 146	-1405463882582
SPT(16)	2310376795707457783	0 40 70 76 148 154 204 208 246 250 300 306 378 384 414 454	-1232193749046
STPT(10)	2310377141371956869	0 2 42 44 60 62 78 80 120 122	-886529249960
SPT(16)	2310377612593462007	0 24 44 84 92 126 140 150 176 186 200 234 242 282 302 326	-415307744822
SPT(16)	2310378033343199623	0 24 30 46 84 100 150 166 228 244 294 310 348 364 370 394	5441992794
SPT(16)	2310378367845777973	0 6 18 28 46 76 94 106 198 210 228 258 276 286 298 304	339944571144
SPT(16)	2310378602710201007	0 6 12 26 32 54 66 74 132 140 152 174 180 194 200 206	574808994178
SPT(16)	2310379179402645653	0 44 150 156 164 176 206 224 360 378 408 420 428 434 540 584	1151501438824
STPT(10)	2310379243506976637	0 2 30 32 72 74 114 116 144 146	1215605769808