Prime p₀= 2807696428908075851 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 40 2 46 2 10 2 106 2 40 2 (?)
a_n: 0 2 66 68 108 110 156 158 168 170 276 278 318 320
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: 320
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 64 40 46 10 106 40

SPT(16)	2807694911908400219	0 14 80 102 114 144 180 192 242 254 290 320 332 354 420 434	-1516999675632
STPT(10)	2807695117026628649	0 2 42 44 60 62 78 80 120 122	-1311881447202
STPT(10)	2807695907095096637	0 2 42 44 72 74 102 104 144 146	-521812979214
TPT(14)	2807696032037954969	0 2 42 44 60 62 72 74 132 134 270 272 300 302	-396870120882
STPT(10)	2807696054732731529	0 2 12 14 90 92 168 170 180 182	-374175344322
TPT(14)	2807696182840909559	0 2 42 44 108 110 168 170 402 404 420 422 432 434	-246067166292
SPT(16)	2807696637582004723	0 10 24 48 66 100 114 118 126 130 144 178 196 220 234 244	208673928872
SPT(16)	2807696741708975687	0 30 42 72 84 110 134 152 162 180 204 230 242 272 284 314	312800899836
STPT(10)	2807697081707176037	0 2 30 32 42 44 54 56 84 86	652799100186
SPT(16)	2807697100776741247	0 46 70 132 156 172 202 222 274 294 324 340 364 426 450 496	671868665396
SPT(16)	2807697334432463533	0 34 54 124 130 144 180 190 228 238 274 288 294 364 384 418	905524387682