Prime p₀= 2623791727985458187 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 58 2 88 2 88 2 64 2 10 2 (?)
a_n: 0 2 24 26 84 86 174 176 264 266 330 332 342 344
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: 344
Found by: RFGuy_KCCO
db: batch=82, k=14, 22 58 88 88 64 10

SPT(16)	2623791215477088731	0 2 26 92 110 128 140 156 182 198 210 228 246 312 336 338	-512508369456
STPT(10)	2623791494575829759	0 2 18 20 30 32 42 44 60 62	-233409628428
SPT(16)	2623791502247043637	0 10 22 40 42 46 60 90 166 196 210 214 216 234 246 256	-225738414550
SPT(16)	2623791582282971063	0 14 96 98 104 126 140 186 218 264 278 300 306 308 390 404	-145702487124
STPT(12)	2623791670477831067	0 2 12 14 42 44 60 62 90 92 102 104	-57507627120
SPT(16)	2623791726195256373	0 44 56 78 170 248 278 294 320 336 366 444 536 558 570 614	-1790201814
SPT(16)	2623791922954500691	0 16 46 60 72 78 100 126 172 198 220 226 238 252 282 298	194969042504
STPT(10)	2623792092167713079	0 2 18 20 30 32 42 44 60 62	364182254892
STPT(10)	2623792376136401891	0 2 36 38 78 80 120 122 156 158	648150943704
STPT(10)	2623792400110558289	0 2 18 20 30 32 42 44 60 62	672125100102
SPT(16)	2623792592456788657	0 6 60 72 76 132 144 150 196 202 214 270 274 286 340 346	864471330470