Prime p₀= 2004206725400386889 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 106 2 40 2 34 2 52 2 (?)
a_n: 0 2 30 32 72 74 180 182 222 224 258 260 312 314
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 314
Found by: Dingo
db: batch=80, k=14, 28 40 106 40 34 52

SPT(16)	2004204972825762059	0 84 108 110 168 222 234 272 300 338 350 404 462 464 488 572	-1752574624830
STPT(10)	2004205314969633791	0 2 36 38 78 80 120 122 156 158	-1410430753098
SPT(16)	2004205897821103217	0 42 44 62 90 92 206 234 272 300 414 416 444 462 464 506	-827579283672
SPT(16)	2004206018152460747	0 30 32 36 50 60 74 80 336 342 356 366 380 384 386 416	-707247926142
SPT(16)	2004206154484786199	0 2 8 110 114 138 168 194 198 224 254 278 282 384 390 392	-570915600690
STPT(10)	2004206214324025331	0 2 6 8 48 50 90 92 96 98	-511076361558
SPT(16)	2004206806264616077	0 10 12 82 94 112 144 154 192 202 234 252 264 334 336 346	80864229188
STPT(10)	2004207361387451201	0 2 36 38 78 80 120 122 156 158	635987064312
STPT(10)	2004207693844826549	0 2 48 50 60 62 72 74 120 122	968444439660
SPT(16)	2004208413474723767	0 12 44 56 72 80 104 114 122 132 156 164 180 192 224 236	1688074336878
STPT(10)	2004208416227461517	0 2 84 86 192 194 300 302 384 386	1690827074628