Prime p₀= 2827087659842599817 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 70 2 328 2 10 2 28 2 214 2 (?)
a_n: 0 2 30 32 102 104 432 434 444 446 474 476 690 692
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: 692
Found by: JayPi
db: batch=82, k=14, 28 70 328 10 28 214

SPT(16)	2827085738938560683	0 20 30 50 78 104 108 114 140 146 150 176 204 224 234 254	-1920904039134
STPT(10)	2827086385394129861	0 2 30 32 60 62 90 92 120 122	-1274448469956
SPT(18)	2827086556473507619	0 18 30 40 48 84 90 120 144 184 208 238 244 280 288 298 310 328	-1103369092198
SPT(16)	2827087303165039997	0 14 24 66 80 92 102 122 144 164 174 186 200 242 252 266	-356677559820
TPT(16)	2827087527507461759	0 2 30 32 48 50 132 134 162 164 288 290 300 302 312 314	-132335138058
SPT(16)	2827087565234794649	0 14 104 128 134 140 144 170 228 254 258 264 270 294 384 398	-94607805168
SPT(16)	2827087718116817371	0 100 138 186 210 220 238 240 418 420 438 448 472 520 558 658	58274217554
SPT(16)	2827087853852693777	0 2 26 30 42 54 86 110 156 180 212 224 236 240 264 266	194010093960
SPT(16)	2827087861396672163	0 6 20 24 56 80 90 120 224 254 264 288 320 324 338 344	201554072346
TPT(14)	2827087917857314649	0 2 102 104 108 110 198 200 312 314 348 350 360 362	258014714832
STPT(10)	2827088012786303171	0 2 6 8 48 50 90 92 96 98	352943703354