Prime p₀= 4506426937906091831 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)	4506424816123268657	0 20 24 42 56 62 66 72 104 110 114 120 134 152 156 176	-2121782823174
SPT(16)	4506425007394610969	0 32 54 78 92 104 120 138 224 242 258 270 284 308 330 362	-1930511480862
SPT(16)	4506425246249639123	0 54 60 68 104 108 116 168 206 258 266 270 306 314 320 374	-1691656452708
STPT(10)	4506426346568181197	0 2 30 32 42 44 54 56 84 86	-591337910634
STPT(10)	4506426589649497619	0 2 42 44 120 122 198 200 240 242	-348256594212
SPT(16)	4506426702330224153	0 6 74 80 84 86 108 144 170 206 228 230 234 240 308 314	-235575867678
STPT(10)	4506426980347422017	0 2 24 26 42 44 60 62 84 86	42441330186
SPT(16)	4506427125142929937	0 4 12 46 54 60 66 96 100 130 136 142 150 184 192 196	187236838106
STPT(10)	4506427230324671957	0 2 30 32 42 44 54 56 84 86	292418580126
STPT(10)	4506427464506245277	0 2 24 26 42 44 60 62 84 86	526600153446
STPT(10)	4506427468632113489	0 2 12 14 90 92 168 170 180 182	530726021658