Prime p₀= 3565551171268725293 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 6 20 28 14 48 12 28 2 28 12 48 14 28 20 6 (?)
a_n: 0 6 26 54 68 116 128 156 158 186 198 246 260 288 308 314
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: 314
Found by: [SG]KidDoesCrunch
db: batch=84, k=16, 6 20 28 14 48 12 28 2

SPT(16)	3565547998326994367	0 30 36 44 114 150 156 210 296 350 356 392 462 470 476 506	-3172941730926
TPT(14)	3565548236343050777	0 2 210 212 240 242 264 266 282 284 330 332 372 374	-2934925674516
TPT(14)	3565549567947253979	0 2 120 122 138 140 180 182 198 200 222 224 240 242	-1603321471314
SPT(16)	3565550084441904719	0 14 24 72 128 132 150 200 222 272 290 294 350 398 408 422	-1086826820574
STPT(10)	3565550239289563541	0 2 30 32 78 80 126 128 156 158	-931979161752
SPT(16)	3565551000643357811	0 12 26 116 150 158 210 236 282 308 360 368 402 492 506 518	-170625367482
STPT(10)	3565551370055329397	0 2 30 32 42 44 54 56 84 86	198786604104
SPT(16)	3565551599083821947	0 12 42 62 66 80 90 174 182 266 276 290 294 314 344 356	427815096654
TPT(14)	3565551658266092951	0 2 30 32 126 128 150 152 210 212 276 278 288 290	486997367658
TPT(14)	3565551684219451349	0 2 12 14 90 92 150 152 222 224 252 254 372 374	512950726056
SPT(16)	3565552429821026069	0 24 50 68 78 84 90 122 150 182 188 194 204 222 248 272	1258552300776