Prime p₀= 1253566007800963979 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 46 2 40 2 40 2 46 2 (?)
a_n: 0 2 48 50 90 92 132 134 180 182
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: 182
Found by: Cruncher Pete
db: batch=77, k=10, 2 46 2 40 2

SPT(16)	1253564418435077527	0 6 10 22 64 106 114 162 184 232 240 282 324 336 340 346	-1589365886452
SPT(16)	1253564441113762213	0 34 60 118 120 130 144 150 154 160 174 184 186 244 270 304	-1566687201766
SPT(16)	1253564942180853059	0 14 18 42 50 72 84 114 128 158 170 192 200 224 228 242	-1065620110920
SPT(16)	1253565156775683733	0 4 24 34 64 78 88 100 288 300 310 324 354 364 384 388	-851025280246
SPT(16)	1253565582692913473	0 8 54 78 84 114 140 168 170 198 224 254 260 284 330 338	-425108050506
SPT(16)	1253565689782899443	0 14 20 84 98 104 110 114 140 144 150 156 170 234 240 254	-318018064536
STPT(10)	1253566272692145857	0 2 30 32 42 44 54 56 84 86	264891181878
STPT(10)	1253566309255846109	0 2 18 20 30 32 42 44 60 62	301454882130
SPT(16)	1253566534256343509	0 12 68 90 98 122 152 158 174 180 210 234 242 264 320 332	526455379530
SPT(16)	1253566579521801211	0 10 112 130 132 150 168 216 322 370 388 406 408 426 528 538	571720837232
SPT(13)	1253566610908246489	0 12 30 138 180 192 210 228 240 282 390 408 420	603107282510