Prime p₀= 2361699609731341001 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 40 2 154 2 10 2 70 2 16 2 (?)
a_n: 0 2 48 50 90 92 246 248 258 260 330 332 348 350
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: 350
Found by: RoXoR
db: batch=81, k=14, 46 40 154 10 70 16

SPT(16)	2361697245711053167	0 4 52 60 66 120 142 166 210 234 256 310 316 324 372 376	-2364020287834
TPT(14)	2361698399412925847	0 2 24 26 72 74 180 182 240 242 294 296 330 332	-1210318415154
SPT(16)	2361698432664491881	0 48 70 100 112 136 148 190 198 240 252 276 288 318 340 388	-1177066849120
STPT(10)	2361698928875169419	0 2 48 50 90 92 132 134 180 182	-680856171582
STPT(10)	2361699130781813687	0 2 12 14 72 74 132 134 144 146	-478949527314
STPT(12)	2361699389740099637	0 2 42 44 90 92 132 134 180 182 222 224	-219991241364
SPT(16)	2361699867081879287	0 20 60 84 110 120 126 186 350 410 416 426 452 476 516 536	257350538286
SPT(16)	2361699898739049403	0 16 36 40 66 120 148 210 304 366 394 448 474 478 498 514	289007708402
SPT(16)	2361699972411478187	0 32 56 140 144 152 164 216 290 342 354 362 366 450 474 506	362680137186
TPT(14)	2361700147272801659	0 2 42 44 78 80 132 134 162 164 198 200 210 212	537541460658
SPT(16)	2361700266732006583	0 10 70 130 160 180 264 294 304 334 418 438 468 528 588 598	657000665582