Prime p₀= 4506323663762413301 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 4 2 40 2 40 2 4 2 (?)
a_n: 0 2 6 8 48 50 90 92 96 98
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: 98
Found by: [SG]KidDoesCrunch
db: batch=85, k=10, 2 4 2 40 2

SPT(16)	4506322658455041299	0 2 44 78 98 128 144 170 192 218 234 264 284 318 360 362	-1005307372002
SPT(16)	4506322668540316051	0 22 138 208 250 252 268 282 388 402 418 420 462 532 648 670	-995222097250
SPT(16)	4506323095616083009	0 10 22 28 52 60 78 100 120 142 160 168 192 198 210 220	-568146330292
SPT(16)	4506323102907535771	0 36 42 60 70 136 138 166 192 220 222 288 298 316 322 358	-560854877530
SPT(16)	4506323154881571341	0 2 26 36 50 66 86 108 110 132 152 168 182 192 216 218	-508880841960
TPT(14)	4506323273971009067	0 2 150 152 192 194 222 224 234 236 264 266 360 362	-389791404234
SPT(16)	4506323814277587707	0 14 54 56 72 86 104 126 170 192 210 224 240 242 282 296	150515174406
SPT(16)	4506324531893298319	0 10 34 52 90 112 168 174 178 184 240 262 300 318 342 352	868130885018
STPT(10)	4506324571120762067	0 2 30 32 42 44 54 56 84 86	907358348766
TPT(14)	4506324582279667757	0 2 54 56 84 86 120 122 162 164 192 194 282 284	918517254456
SPT(16)	4506324612299496191	0 8 20 30 32 62 66 122 126 182 186 216 218 228 240 248	948537082890