Prime p₀= 4387619626905037319 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 16 2 10 2 10 2 16 2 (?)
a_n: 0 2 18 20 30 32 42 44 60 62
All 10 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 62
Found by: [SG]KidDoesCrunch
db: batch=85, k=10, 2 16 2 10 2

SPT(16)	4387618473617656063	0 24 66 76 78 94 96 120 154 178 180 196 198 208 250 274	-1153287381256
STPT(10)	4387618550790583349	0 2 42 44 90 92 138 140 180 182	-1076114453970
SPT(16)	4387618957178658973	0 24 28 30 84 100 118 136 168 186 204 220 274 276 280 304	-669726378346
STPT(10)	4387619021520644549	0 2 12 14 90 92 168 170 180 182	-605384392770
STPT(10)	4387619086453895021	0 2 36 38 78 80 120 122 156 158	-540451142298
SPT(16)	4387619504251010257	0 10 16 24 112 154 184 192 214 222 252 294 382 390 396 406	-122654027062
TPT(14)	4387620043451783441	0 2 18 20 30 32 78 80 156 158 198 200 246 248	416546746122
SPT(16)	4387620415132262593	0 6 18 28 36 84 96 106 318 328 340 388 396 406 418 424	788227225274
STPT(10)	4387620857222095037	0 2 30 32 42 44 54 56 84 86	1230317057718
TPT(14)	4387621269755821169	0 2 18 20 48 50 72 74 282 284 288 290 312 314	1642850783850
STPT(10)	4387621558406512709	0 2 48 50 90 92 132 134 180 182	1931501475390