Prime p₀= 3091599109341194237 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 76 2 10 2 106 2 40 2 10 2 (?)
a_n: 0 2 42 44 120 122 132 134 240 242 282 284 294 296
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: 296
Found by: suriv
db: batch=83, k=14, 40 76 10 106 40 10

SPT(16)	3091596675884782907	0 74 80 116 122 144 162 204 212 254 272 294 300 336 342 416	-2433456411330
TPT(14)	3091597175679588221	0 2 18 20 60 62 90 92 120 122 198 200 246 248	-1933661606016
SPT(16)	3091597876351179359	0 8 42 62 104 110 132 150 152 170 192 198 240 260 294 302	-1232990014878
STPT(10)	3091598322970620311	0 2 30 32 60 62 90 92 120 122	-786370573926
SPT(16)	3091598720977309549	0 4 12 52 90 100 130 144 208 222 252 262 300 340 348 352	-388363884688
TPT(14)	3091599067770165941	0 2 6 8 18 20 30 32 216 218 258 260 330 332	-41571028296
SPT(16)	3091599326487135073	0 10 16 24 54 58 148 150 184 186 276 280 310 318 324 334	217145940836
STPT(10)	3091599629629151549	0 2 18 20 30 32 42 44 60 62	520287957312
SPT(16)	3091599640165393867	0 30 34 46 72 100 102 132 154 184 186 214 240 252 256 286	530824199630
STPT(10)	3091599796280611739	0 2 12 14 30 32 48 50 60 62	686939417502
SPT(16)	3091600324668804367	0 4 24 82 90 144 160 174 220 234 250 304 312 370 390 394	1215327610130