Prime p₀= 2777820814572922289 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 28 2 34 2 82 2 88 2 94 2 (?)
a_n: 0 2 12 14 42 44 78 80 162 164 252 254 348 350
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: 350
Found by: Orange Kid
db: batch=82, k=14, 10 28 34 82 88 94

SPT(16)	2777818973822919029	0 12 42 104 108 122 132 138 164 170 180 194 198 260 290 302	-1840750003260
SPT(16)	2777819516498103263	0 14 30 54 90 98 134 138 296 300 336 344 380 404 420 434	-1298074819026
SPT(16)	2777819553653116249	0 4 12 18 34 54 78 138 154 214 238 258 274 280 288 292	-1260919806040
SPT(16)	2777819687565133361	0 56 68 78 86 90 138 218 300 380 428 432 440 450 462 518	-1127007788928
STPT(10)	2777820288675616937	0 2 30 32 42 44 54 56 84 86	-525897305352
SPT(16)	2777820337853695499	0 54 72 84 92 110 150 162 200 212 252 270 278 290 308 362	-476719226790
STPT(10)	2777821072692849509	0 2 18 20 30 32 42 44 60 62	258119927220
STPT(10)	2777821528399586477	0 2 12 14 42 44 72 74 84 86	713826664188
SPT(16)	2777821707400623883	0 28 54 58 88 96 138 186 238 286 328 336 366 370 396 424	892827701594
STPT(10)	2777821934086600787	0 2 12 14 42 44 72 74 84 86	1119513678498
SPT(16)	2777821995087302543	0 44 48 80 86 156 164 198 266 300 308 378 384 416 420 464	1180514380254