Prime p₀= 1124852269355316347 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)	1124851442552278849	0 4 30 42 70 78 84 118 144 178 184 192 220 232 258 262	-826803037498
SPT(16)	1124851650378542147	0 6 32 42 50 84 116 122 144 150 182 216 224 234 260 266	-618976774200
SPT(16)	1124851671327386971	0 30 42 52 66 90 100 112 156 168 178 202 216 226 238 268	-598027929376
SPT(16)	1124852074593367969	0 4 10 34 72 90 120 150 154 184 214 232 270 294 300 304	-194761948378
TPT(14)	1124852250838546331	0 2 48 50 78 80 138 140 168 170 288 290 336 338	-18516770016
STPT(10)	1124852259331237709	0 2 18 20 30 32 42 44 60 62	-10024078638
SPT(16)	1124852366801097859	0 4 30 58 70 78 114 130 162 178 214 222 234 262 288 292	97445781512
STPT(10)	1124852403656154959	0 2 30 32 60 62 90 92 120 122	134300838612
STPT(10)	1124852535242885789	0 2 18 20 30 32 42 44 60 62	265887569442
SPT(16)	1124852860167704537	0 2 56 72 74 80 90 102 104 116 126 132 134 150 204 206	590812388190
STPT(10)	1124852872400445647	0 2 30 32 42 44 54 56 84 86	603045129300