Prime p₀= 1124853599103342107 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 22 2 16 2 16 2 22 2 (?)
a_n: 0 2 24 26 42 44 60 62 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: crashtech
db: batch=76, k=10, 2 22 2 16 2

SPT(16)	1124852366801097859	0 4 30 58 70 78 114 130 162 178 214 222 234 262 288 292	-1232302244248
STPT(10)	1124852403656154959	0 2 30 32 60 62 90 92 120 122	-1195447187148
STPT(10)	1124852535242885789	0 2 18 20 30 32 42 44 60 62	-1063860456318
SPT(16)	1124852860167704537	0 2 56 72 74 80 90 102 104 116 126 132 134 150 204 206	-738935637570
STPT(10)	1124852872400445647	0 2 30 32 42 44 54 56 84 86	-726702896460
SPT(16)	1124852944355840627	0 32 42 72 74 116 120 146 240 266 270 312 314 344 354 386	-654747501480
SPT(16)	1124854013769391417	0 46 124 150 156 172 180 186 220 226 234 250 256 282 360 406	414666049310
SPT(16)	1124854199793587443	0 34 48 78 136 148 190 204 250 264 306 318 376 406 420 454	600690245336
SPT(16)	1124854370006977537	0 22 90 96 102 144 156 246 250 340 352 394 400 406 474 496	770903635430
TPT(14)	1124854657468562261	0 2 168 170 258 260 300 302 306 308 336 338 348 350	1058365220154
STPT(10)	1124854680178059659	0 2 12 14 90 92 168 170 180 182	1081074717552