Prime p₀= 3717733392401626571 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 76 2 58 2 58 2 76 2 (?)
a_n: 0 2 78 80 138 140 198 200 276 278
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: 278
Found by: Sphynx
db: batch=84, k=10, 2 76 2 58 2

SPT(16)	3717732368051779967	0 14 32 36 54 96 102 110 126 134 140 182 200 204 222 236	-1024349846604
STPT(10)	3717732687855751151	0 2 108 110 138 140 168 170 276 278	-704545875420
SPT(16)	3717732711996925429	0 34 70 78 114 118 150 162 190 202 234 238 274 282 318 352	-680404701142
STPT(10)	3717732775714440149	0 2 42 44 60 62 78 80 120 122	-616687186422
STPT(10)	3717733058865523667	0 2 30 32 72 74 114 116 144 146	-333536102904
STPT(10)	3717733080890382857	0 2 30 32 120 122 210 212 240 242	-311511243714
STPT(12)	3717733429803004481	0 2 18 20 60 62 156 158 198 200 216 218	37401377910
SPT(13)	3717733628805077977	0 36 72 132 156 162 186 210 216 240 300 336 372	236403451406
STPT(10)	3717733927464249179	0 2 12 14 90 92 168 170 180 182	535062622608
SPT(16)	3717733997035578323	0 14 26 38 44 84 86 90 104 108 110 150 156 168 180 194	604633951752
SPT(16)	3717734197294691557	0 54 84 144 156 162 196 202 294 300 334 340 352 412 442 496	804893064986