Prime p₀= 2356042313449328417 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 28 2 58 2 166 2 76 2 58 2 (?)
a_n: 0 2 84 86 114 116 174 176 342 344 420 422 480 482
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: 482
Found by: ChUcK
db: batch=81, k=14, 82 28 58 166 76 58

SPT(16)	2356040890855698463	0 4 6 28 46 96 114 118 126 130 148 198 216 238 240 244	-1422593629954
SPT(20)	2356041477294947417	0 6 24 44 62 86 122 180 224 290 306 372 416 474 510 534 552 572 590 596	-836154381000
TPT(14)	2356041676317265829	0 2 60 62 300 302 312 314 378 380 390 392 462 464	-637132062588
SPT(16)	2356041795635839951	0 12 40 58 82 106 138 222 226 310 342 366 390 408 436 448	-517813488466
SPT(16)	2356042234192350659	0 30 42 50 74 98 120 134 138 152 174 198 222 230 242 272	-79256977758
SPT(16)	2356042280754558203	0 20 36 56 78 114 146 170 174 198 230 266 288 308 324 344	-32694770214
SPT(16)	2356042569104858947	0 4 46 112 144 154 186 280 306 400 432 442 474 540 582 586	255655530530
STPT(10)	2356042887470900627	0 2 24 26 42 44 60 62 84 86	574021572210
SPT(16)	2356043534035704719	0 62 72 108 152 164 240 252 260 272 348 360 404 440 450 512	1220586376302
SPT(16)	2356043635907625271	0 40 48 58 76 88 90 100 126 136 138 150 168 178 186 226	1322458296854
STPT(10)	2356043735980900751	0 2 30 32 60 62 90 92 120 122	1422531572334