Prime p₀= 2004204634304596781 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 46 2 46 2 28 2 (?)
a_n: 0 2 30 32 78 80 126 128 156 158
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: 158
Found by: Landjunge
db: batch=80, k=10, 2 28 2 46 2

SPT(16)	2004203396894929849	0 22 34 54 58 112 114 132 190 208 210 264 268 288 300 322	-1237409666932
TPT(14)	2004203438532071087	0 2 174 176 234 236 372 374 420 422 462 464 510 512	-1195772525694
TPT(14)	2004203517179410667	0 2 24 26 30 32 72 74 84 86 150 152 180 182	-1117125186114
SPT(16)	2004203755335365917	0 12 64 82 156 172 180 204 232 256 264 280 354 372 424 436	-878969230864
SPT(16)	2004203934826759537	0 4 34 54 70 76 84 100 156 172 180 186 202 222 252 256	-699477837244
SPT(16)	2004203956028620573	0 16 30 66 78 84 106 118 156 168 190 196 208 244 258 274	-678275976208
SPT(16)	2004204853233153523	0 24 54 64 88 124 148 168 250 270 294 330 354 364 394 418	218928556742
SPT(16)	2004204972825762059	0 84 108 110 168 222 234 272 300 338 350 404 462 464 488 572	338521165278
STPT(10)	2004205314969633791	0 2 36 38 78 80 120 122 156 158	680665037010
SPT(16)	2004205897821103217	0 42 44 62 90 92 206 234 272 300 414 416 444 462 464 506	1263516506436
SPT(16)	2004206018152460747	0 30 32 36 50 60 74 80 336 342 356 366 380 384 386 416	1383847863966