Prime p₀= 1296906558223099007 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 28 2 28 2 28 2 (?)
a_n: 0 2 30 32 60 62 90 92 120 122
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: 122
Found by: Cruncher Pete
db: batch=77, k=10, 2 28 2 28 2

SPT(16)	1296905781899559641	0 18 32 78 80 98 102 108 110 116 120 138 140 186 200 218	-776323539366
STPT(12)	1296905925519746207	0 2 12 14 24 26 30 32 42 44 54 56	-632703352800
TPT(14)	1296905925519746207	0 2 12 14 24 26 30 32 42 44 54 56 180 182	-632703352800
STPT(10)	1296906015364725707	0 2 30 32 42 44 54 56 84 86	-542858373300
SPT(16)	1296906144342901451	0 2 20 56 60 62 72 86 102 116 126 128 132 168 186 188	-413880197556
STPT(10)	1296906457997520707	0 2 30 32 42 44 54 56 84 86	-100225578300
SPT(16)	1296906621691214291	0 38 66 72 116 128 150 170 198 218 240 252 296 302 330 368	63468115284
SPT(16)	1296906940127711903	0 6 14 48 104 110 138 144 170 176 204 210 266 300 308 314	381904612896
STPT(10)	1296907137686338427	0 2 12 14 42 44 72 74 84 86	579463239420
SPT(16)	1296907310847032107	0 4 42 112 114 130 136 142 144 150 156 172 174 244 282 286	752623933100
SPT(16)	1296907866862194569	0 2 30 54 78 120 132 140 162 170 182 224 248 272 300 302	1308639095562