Prime p₀= 4506323102907535771 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 36 6 18 10 66 2 28 26 28 2 66 10 18 6 36 (?)
a_n: 0 36 42 60 70 136 138 166 192 220 222 288 298 316 322 358
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: 358
Found by: [SG]KidDoesCrunch
db: batch=85, k=16, 36 6 18 10 66 2 28 26

STPT(12)	4506321363582501719	0 2 12 14 18 20 42 44 48 50 60 62	-1739325034052
STPT(10)	4506322379330903039	0 2 18 20 30 32 42 44 60 62	-723576632732
SPT(16)	4506322403938451489	0 92 120 158 162 182 252 282 338 368 438 458 462 500 528 620	-698969084282
SPT(16)	4506322658455041299	0 2 44 78 98 128 144 170 192 218 234 264 284 318 360 362	-444452494472
SPT(16)	4506322668540316051	0 22 138 208 250 252 268 282 388 402 418 420 462 532 648 670	-434367219720
SPT(16)	4506323095616083009	0 10 22 28 52 60 78 100 120 142 160 168 192 198 210 220	-7291452762
SPT(16)	4506323154881571341	0 2 26 36 50 66 86 108 110 132 152 168 182 192 216 218	51974035570
TPT(14)	4506323273971009067	0 2 150 152 192 194 222 224 234 236 264 266 360 362	171063473296
STPT(10)	4506323663762413301	0 2 6 8 48 50 90 92 96 98	560854877530
SPT(16)	4506323814277587707	0 14 54 56 72 86 104 126 170 192 210 224 240 242 282 296	711370051936
SPT(16)	4506324531893298319	0 10 34 52 90 112 168 174 178 184 240 262 300 318 342 352	1428985762548