Prime p₀= 2871514437544852577 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 130 2 40 2 34 2 70 2 88 2 178 2 (?)
a_n: 0 2 132 134 174 176 210 212 282 284 372 374 552 554
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: 554
Found by: JayPi
db: batch=82, k=14, 130 40 34 70 88 178

TPT(14)	2871512985614622827	0 2 30 32 240 242 342 344 372 374 450 452 492 494	-1451930229750
SPT(16)	2871513060024970441	0 12 28 70 90 148 168 178 192 202 222 280 300 342 358 370	-1377519882136
STPT(10)	2871513068919071999	0 2 42 44 120 122 198 200 240 242	-1368625780578
SPT(16)	2871513153380304413	0 8 36 38 84 110 140 164 210 234 264 290 336 338 366 374	-1284164548164
SPT(16)	2871513843436718323	0 18 34 64 78 90 114 148 180 214 238 250 264 294 310 328	-594108134254
TPT(14)	2871514173133287971	0 2 18 20 78 80 90 92 156 158 168 170 186 188	-264411564606
TPT(14)	2871514565484313037	0 2 42 44 84 86 102 104 120 122 210 212 324 326	127939460460
SPT(16)	2871514712373532831	0 16 22 42 60 88 132 162 166 196 240 268 286 306 312 328	274828680254
SPT(16)	2871514758989210441	0 56 66 90 108 170 182 216 242 276 288 350 368 392 402 458	321444357864
SPT(16)	2871514865732992351	0 22 60 90 108 166 208 228 280 300 342 400 418 448 486 508	428188139774
SPT(16)	2871515192183960447	0 60 110 152 156 180 192 236 240 284 296 320 324 366 416 476	754639107870