Prime p₀= 2127775509888368297 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 58 2 118 2 10 2 4 2 28 2 (?)
a_n: 0 2 42 44 102 104 222 224 234 236 240 242 270 272
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: 272
Found by: retroactivemind
db: batch=80, k=14, 40 58 118 10 4 28

SPT(16)	2127773691994800761	0 66 72 170 186 212 246 260 282 296 330 356 372 470 476 542	-1817893567536
STPT(10)	2127773934055978067	0 2 30 32 72 74 114 116 144 146	-1575832390230
SPT(16)	2127774798135103501	0 18 48 66 72 88 90 112 156 178 180 196 202 220 250 268	-711753264796
SPT(16)	2127774900205708531	0 40 42 82 112 150 196 250 252 306 352 390 420 460 462 502	-609682659766
SPT(16)	2127775442266082953	0 10 16 18 58 70 88 108 148 168 186 198 238 240 246 256	-67622285344
STPT(10)	2127775462247582669	0 2 18 20 30 32 42 44 60 62	-47640785628
STPT(10)	2127776041200872771	0 2 36 38 78 80 120 122 156 158	531312504474
SPT(16)	2127776092148272109	0 8 18 42 68 74 122 150 152 180 228 234 260 284 294 302	582259903812
SPT(16)	2127776691641868661	0 102 106 142 172 192 270 286 312 328 406 426 456 492 496 598	1181753500364
STPT(10)	2127776773222252037	0 2 12 14 42 44 72 74 84 86	1263333883740
SPT(16)	2127777104585174453	0 8 38 48 66 90 104 108 206 210 224 248 266 276 306 314	1594696806156