Prime p₀= 2097879582365819267 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 16 2 148 2 10 2 16 2 40 2 (?)
a_n: 0 2 54 56 72 74 222 224 234 236 252 254 294 296
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: JonS
db: batch=80, k=14, 52 16 148 10 16 40

TPT(14)	2097878076482740997	0 2 54 56 84 86 90 92 102 104 210 212 264 266	-1505883078270
STPT(10)	2097878111154104759	0 2 18 20 30 32 42 44 60 62	-1471211714508
SPT(16)	2097878507963511677	0 42 50 60 62 144 152 162 164 174 182 264 266 276 284 326	-1074402307590
STPT(12)	2097878633295889139	0 2 48 50 78 80 222 224 252 254 300 302	-949069930128
SPT(16)	2097878733630546247	0 24 42 54 72 76 90 142 174 226 240 244 262 274 292 316	-848735273020
SPT(16)	2097879362141373919	0 12 42 52 54 58 84 118 174 208 234 238 240 250 280 292	-220224445348
SPT(16)	2097880045453324711	0 10 18 40 88 102 106 138 160 192 196 210 258 280 288 298	463087505444
STPT(10)	2097880891260787769	0 2 42 44 90 92 138 140 180 182	1308894968502
STPT(10)	2097880895737684007	0 2 30 32 42 44 54 56 84 86	1313371864740
STPT(10)	2097880957142564117	0 2 30 32 42 44 54 56 84 86	1374776744850
SPT(16)	2097881119489372559	0 18 128 158 194 210 248 264 338 354 392 408 444 474 584 602	1537123553292