Prime p₀= 1237936718650006337 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: Cruncher Pete
db: batch=77, k=10, 2 28 2 10 2

SPT(16)	1237934656637305909	0 18 22 24 34 60 64 90 232 258 262 288 298 300 304 322	-2062012700428
SPT(16)	1237934689641442537	0 6 64 70 106 132 150 156 160 166 184 210 246 252 310 316	-2029008563800
SPT(16)	1237935298757717587	0 10 30 34 46 52 84 100 186 202 234 240 252 256 276 286	-1419892288750
STPT(10)	1237935695013962447	0 2 24 26 42 44 60 62 84 86	-1023636043890
SPT(16)	1237935777330469999	0 12 48 70 112 148 150 192 220 262 264 300 342 364 400 412	-941319536338
TPT(14)	1237936234229152121	0 2 96 98 138 140 186 188 198 200 210 212 240 242	-484420854216
STPT(10)	1237936795551951107	0 2 30 32 42 44 54 56 84 86	76901944770
SPT(16)	1237937002827808441	0 12 46 72 82 112 120 130 138 148 156 186 196 222 256 268	284177802104
STPT(10)	1237937077095251747	0 2 30 32 42 44 54 56 84 86	358445245410
TPT(14)	1237937191860377597	0 2 12 14 42 44 114 116 120 122 210 212 252 254	473210371260
SPT(16)	1237937446437365189	0 24 32 54 90 98 102 110 222 230 234 242 278 300 308 332	727787358852