Prime p₀= 1117000816116119687 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: mikey
db: batch=76, k=10, 2 28 2 10 2

SPT(16)	1116999539293848013	0 16 18 24 30 88 94 108 136 150 156 214 220 226 228 244	-1276822271674
STPT(10)	1116999823880549639	0 2 30 32 60 62 90 92 120 122	-992235570048
TPT(14)	1117000183221828641	0 2 168 170 360 362 366 368 390 392 456 458 498 500	-632894291046
SPT(15)	1117000262578985923	0 6 24 36 66 120 144 210 276 300 354 384 396 414 420	-553537133764
SPT(16)	1117000357502967599	0 2 12 44 50 62 72 120 194 242 252 264 270 302 312 314	-458613152088
STPT(10)	1117000484547423569	0 2 30 32 120 122 210 212 240 242	-331568696118
SPT(16)	1117000851753756517	0 6 22 34 64 84 94 100 126 132 142 162 192 204 220 226	35637636830
STPT(10)	1117001245964811797	0 2 42 44 72 74 102 104 144 146	429848692110
STPT(10)	1117001632516531589	0 2 42 44 60 62 78 80 120 122	816400411902
STPT(10)	1117001793823261847	0 2 54 56 72 74 90 92 144 146	977707142160
SPT(16)	1117001847209165527	0 4 24 36 46 52 60 82 84 106 114 120 130 142 162 166	1031093045840