Prime p₀= 2323347356894976077 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 10 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 54 56 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: Landjunge
db: batch=81, k=10, 2 28 2 10 2

SPT(16)	2323346802985919423	0 6 14 56 60 84 104 116 138 150 170 194 198 240 248 254	-553909056654
STPT(10)	2323346969583124781	0 2 6 8 18 20 30 32 36 38	-387311851296
STPT(10)	2323346980334986181	0 2 36 38 78 80 120 122 156 158	-376559989896
SPT(16)	2323347074552369989	0 48 84 88 90 118 132 184 198 250 264 292 294 298 334 382	-282342606088
SPT(16)	2323347110500291321	0 66 78 96 120 160 166 216 322 372 378 418 442 460 472 538	-246394684756
STPT(10)	2323347309026309339	0 2 48 50 90 92 132 134 180 182	-47868666738
STPT(10)	2323347632321284367	0 2 30 32 42 44 54 56 84 86	275426308290
STPT(10)	2323347707253065327	0 2 30 32 102 104 174 176 204 206	350358089250
SPT(16)	2323347739830379811	0 48 72 86 126 128 146 152 156 162 180 182 222 236 260 308	382935403734
TPT(14)	2323348058523330689	0 2 48 50 90 92 102 104 168 170 210 212 270 272	701628354612
TPT(14)	2323348072485685757	0 2 12 14 24 26 30 32 72 74 114 116 150 152	715590709680