Prime p₀= 2787669797714725739 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 16 2 16 2 10 2 (?)
a_n: 0 2 12 14 30 32 48 50 60 62
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: 62
Found by: [SG]ATA-Rolf
db: batch=82, k=10, 2 10 2 16 2

SPT(16)	2787667668244923287	0 20 54 80 120 162 192 252 272 332 362 404 444 470 504 524	-2129469802452
SPT(16)	2787669084073662443	0 20 44 78 114 120 128 134 174 180 188 194 230 264 288 308	-713641063296
SPT(16)	2787669232669604719	0 10 28 30 34 42 52 112 150 210 220 228 232 234 252 262	-565045121020
SPT(16)	2787669250439228443	0 4 60 78 100 106 120 136 198 214 228 234 256 274 330 334	-547275497296
SPT(16)	2787669270861437663	0 8 26 30 44 50 54 116 138 200 204 210 224 228 246 254	-526853288076
STPT(10)	2787669332571309881	0 2 30 32 78 80 126 128 156 158	-465143415858
STPT(10)	2787669902624370089	0 2 18 20 30 32 42 44 60 62	104909644350
STPT(10)	2787670006188796637	0 2 30 32 42 44 54 56 84 86	208474070898
SPT(16)	2787670920784950071	0 20 78 132 188 216 222 240 368 386 392 420 476 530 588 608	1123070224332
SPT(16)	2787671101961559041	0 12 18 26 30 68 86 116 222 252 270 308 312 320 326 338	1304246833302
STPT(10)	2787671131215342719	0 2 42 44 90 92 138 140 180 182	1333500616980