Prime p₀= 4387504089218955751 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 12 4 12 8 4 6 2 22 2 6 4 8 12 4 12 (?)
a_n: 0 12 16 28 36 40 46 48 70 72 78 82 90 102 106 118
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: 118
Found by: [SG]KidDoesCrunch
db: batch=85, k=16, 12 4 12 8 4 6 2 22

SPT(16)	4387501228682631863	0 20 30 44 56 90 96 138 146 188 194 228 240 254 264 284	-2860536323888
STPT(10)	4387501900420013729	0 2 48 50 90 92 132 134 180 182	-2188798942022
STPT(10)	4387502862469386761	0 2 6 8 48 50 90 92 96 98	-1226749568990
STPT(10)	4387503494646759959	0 2 42 44 90 92 138 140 180 182	-594572195792
SPT(16)	4387503687291773413	0 30 46 54 78 96 154 156 178 180 238 256 280 288 304 334	-401927182338
SPT(16)	4387503732681102893	0 90 104 114 116 150 168 234 290 356 374 408 410 420 434 524	-356537852858
STPT(10)	4387504623411344387	0 2 30 32 42 44 54 56 84 86	534192388636
STPT(10)	4387505142996338681	0 2 36 38 108 110 180 182 216 218	1053777382930
SPT(16)	4387505181254518483	0 6 24 28 30 94 144 196 198 250 300 364 366 370 388 394	1092035562732
SPT(16)	4387505489668879033	0 4 24 66 78 100 144 210 334 400 444 466 478 520 540 544	1400449923282
STPT(10)	4387505603711992427	0 2 30 32 42 44 54 56 84 86	1514493036676