Prime p₀= 2812509210273276797 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 28 2 34 2 40 2 46 2 22 2 (?)
a_n: 0 2 24 26 54 56 90 92 132 134 180 182 204 206
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: 206
Found by: [SG-FC] hl
db: batch=82, k=14, 22 28 34 40 46 22

SPT(16)	2812506690446643989	0 14 68 78 120 140 164 170 192 198 222 242 284 294 348 362	-2519826632808
STPT(10)	2812507341218148059	0 2 48 50 90 92 132 134 180 182	-1869055128738
STPT(10)	2812507754061160451	0 2 6 8 18 20 30 32 36 38	-1456212116346
SPT(16)	2812508537049768047	0 2 30 54 66 72 86 96 140 150 164 170 182 206 234 236	-673223508750
SPT(16)	2812508586874511927	0 6 20 24 36 54 80 110 120 150 176 194 206 210 224 230	-623398764870
SPT(16)	2812508951211708641	0 6 36 68 146 156 170 188 210 228 242 252 330 362 392 398	-259061568156
SPT(16)	2812509261917602463	0 20 24 30 150 164 188 194 210 216 240 254 374 380 384 404	51644325666
STPT(10)	2812509476923469471	0 2 30 32 78 80 126 128 156 158	266650192674
SPT(16)	2812509523487144737	0 34 40 154 180 210 214 244 300 330 334 364 390 504 510 544	313213867940
STPT(10)	2812509567604823417	0 2 60 62 102 104 144 146 204 206	357331546620
SPT(16)	2812509867291382163	0 14 48 50 66 104 126 138 206 218 240 278 294 296 330 344	657018105366