Prime p₀= 4503953820245513087 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 22 2 16 2 16 2 22 2 (?)
a_n: 0 2 24 26 42 44 60 62 84 86
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: 86
Found by: [SG]KidDoesCrunch
db: batch=85, k=10, 2 22 2 16 2

TPT(14)	4503952448047788479	0 2 18 20 30 32 42 44 102 104 168 170 198 200	-1372197724608
SPT(16)	4503952654553622211	0 22 40 82 96 100 112 132 190 210 222 226 240 282 300 322	-1165691890876
SPT(16)	4503952725031255631	0 32 36 50 56 62 66 90 92 116 120 126 132 146 150 182	-1095214257456
STPT(10)	4503953075049998621	0 2 6 8 18 20 30 32 36 38	-745195514466
SPT(16)	4503953539062090007	0 16 30 52 82 96 100 126 196 222 226 240 270 292 306 322	-281183423080
SPT(16)	4503953629627169197	0 34 76 82 120 126 130 132 154 156 160 166 204 210 252 286	-190618343890
STPT(10)	4503954007397676497	0 2 12 14 42 44 72 74 84 86	187152163410
STPT(10)	4503954145293506087	0 2 30 32 60 62 90 92 120 122	325047993000
STPT(10)	4503955026977520857	0 2 12 14 42 44 72 74 84 86	1206732007770
STPT(10)	4503955032560796257	0 2 30 32 42 44 54 56 84 86	1212315283170
STPT(10)	4503955838099541149	0 2 18 20 30 32 42 44 60 62	2017854028062