Prime p₀= 1296904624973138627 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 6 18 60 48 8 6 30 4 30 6 8 48 60 18 6 (?)
a_n: 0 6 24 84 132 140 146 176 180 210 216 224 272 332 350 356
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: 356
Found by: Cruncher Pete
db: batch=77, k=16, 6 18 60 48 8 6 30 4

SPT(16)	1296902742675954539	0 42 48 98 110 114 138 192 230 284 308 312 324 374 380 422	-1882297184088
STPT(10)	1296903164622666449	0 2 30 32 60 62 90 92 120 122	-1460350472178
SPT(16)	1296903287015662063	0 78 118 136 138 150 196 238 288 330 376 388 390 408 448 526	-1337957476564
TPT(14)	1296904011363498281	0 2 18 20 30 32 78 80 168 170 198 200 210 212	-613609640346
SPT(16)	1296904136765408557	0 12 40 42 46 52 60 66 130 136 144 150 154 156 184 196	-488207730070
STPT(10)	1296904386772379387	0 2 30 32 60 62 90 92 120 122	-238200759240
SPT(16)	1296905026474252193	0 20 56 60 84 104 126 140 150 164 186 206 230 234 270 290	401501113566
STPT(10)	1296905177885648699	0 2 18 20 30 32 42 44 60 62	552912510072
SPT(16)	1296905530983693859	0 70 78 88 100 120 198 250 288 340 418 438 450 460 468 538	906010555232
STPT(10)	1296905540222258171	0 2 6 8 18 20 30 32 36 38	915249119544
SPT(16)	1296905769028641913	0 10 16 30 40 58 78 136 378 436 456 474 484 498 504 514	1144055503286