Prime p₀= 2829625491767317349 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 88 2 16 2 10 2 46 2 40 2 (?)
a_n: 0 2 30 32 120 122 138 140 150 152 198 200 240 242
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: 242
Found by: JayPi
db: batch=82, k=14, 28 88 16 10 46 40

SPT(16)	2829624697822728863	0 36 66 78 120 128 150 158 168 176 198 206 248 260 290 326	-793944588486
TPT(14)	2829624750346677929	0 2 18 20 42 44 90 92 258 260 372 374 378 380	-741420639420
SPT(16)	2829625029298756307	0 14 36 62 80 86 164 192 194 222 300 306 324 350 372 386	-462468561042
SPT(16)	2829625175449444651	0 70 82 90 142 166 208 240 268 300 342 366 418 426 438 508	-316317872698
SPT(16)	2829625186750491263	0 14 38 60 128 150 168 180 224 236 254 276 344 366 390 404	-305016826086
SPT(16)	2829625339229602817	0 14 54 134 186 264 296 320 420 444 476 554 606 686 726 740	-152537714532
SPT(16)	2829625748629822903	0 54 76 94 96 126 150 160 270 280 304 334 336 354 376 430	256862505554
STPT(10)	2829625825437517217	0 2 42 44 72 74 102 104 144 146	333670199868
SPT(16)	2829625915034380291	0 18 46 76 96 162 232 238 300 306 376 442 462 492 520 538	423267062942
SPT(16)	2829626133438256799	0 12 20 50 80 138 272 300 422 450 584 642 672 702 710 722	641670939450
STPT(10)	2829626537550889157	0 2 54 56 72 74 90 92 144 146	1045783571808