Prime p₀= 6129507724234637 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 28 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 72 74 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: paulteo
db: batch=62, k=10, 2 10 2 28 2

SPT(14)	6129463370016757	0 12 30 46 52 82 84 112 114 144 150 166 184 196	-44354217880
TPT(12)	6129466638045689	0 2 42 44 78 80 108 110 288 290 402 404	-41086188948
SPT(14)	6129469004924453	0 6 14 48 84 128 140 144 156 200 236 270 278 284	-38719310184
SPT(14)	6129484333457671	0 28 72 82 90 118 138 142 162 190 198 208 252 280	-23390776966
SPT(14)	6129487734238009	0 10 18 58 64 70 78 94 102 108 114 154 162 172	-19989996628
SPT(14)	6129495539982677	0 14 32 56 80 104 120 146 162 186 210 234 252 266	-12184251960
SPT(14)	6129509189120311	0 10 12 18 52 78 102 106 130 156 190 196 198 208	1464885674
SPT(14)	6129514483409953	0 16 34 48 60 76 84 130 138 154 166 180 198 214	6759175316
SPT(14)	6129528266878067	0 2 20 42 44 62 90 164 192 210 212 234 252 254	20542643430
SPT(14)	6129529036333037	0 56 86 126 132 140 144 152 156 164 170 210 240 296	21312098400
SPT(14)	6129529524900121	0 40 42 70 96 120 130 138 148 172 198 226 228 268	21800665484