Prime p₀= 2777809032582112211 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 106 2 10 2 4 2 52 2 76 2 (?)
a_n: 0 2 90 92 198 200 210 212 216 218 270 272 348 350
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: JayPi
db: batch=82, k=14, 88 106 10 4 52 76

SPT(16)	2777808369947000927	0 20 50 54 96 104 110 176 180 246 252 260 302 306 336 356	-662635111284
STPT(10)	2777808470815068917	0 2 30 32 72 74 114 116 144 146	-561767043294
TPT(14)	2777808668335153667	0 2 12 14 54 56 90 92 102 104 132 134 144 146	-364246958544
STPT(10)	2777808714634029257	0 2 24 26 42 44 60 62 84 86	-317948082954
SPT(16)	2777808856654575853	0 54 64 88 118 126 148 214 240 306 328 336 366 390 400 454	-175927536358
STPT(10)	2777808857496802901	0 2 30 32 78 80 126 128 156 158	-175085309310
STPT(10)	2777809170945366791	0 2 36 38 78 80 120 122 156 158	138363254580
STPT(10)	2777809645932025259	0 2 18 20 60 62 102 104 120 122	613349913048
STPT(12)	2777809734973553219	0 2 30 32 60 62 102 104 132 134 162 164	702391441008
SPT(16)	2777809808458982659	0 52 82 94 118 154 172 234 238 300 318 354 378 390 420 472	775876870448
SPT(18)	2777810134256007401	0 36 62 102 132 146 150 162 180 188 206 218 222 236 266 306 332 368	1101673895190