Prime p₀= 2142412796425789289 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 52 2 4 2 40 2 136 2 52 2 (?)
a_n: 0 2 78 80 132 134 138 140 180 182 318 320 372 374
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: 374
Found by: KAMCOBILL
db: batch=80, k=14, 76 52 4 40 136 52

SPT(16)	2142411692465422457	0 14 56 62 74 80 140 164 192 216 276 282 294 300 342 356	-1103960366832
STPT(10)	2142412077569882087	0 2 54 56 72 74 90 92 144 146	-718855907202
STPT(10)	2142412087504330259	0 2 48 50 60 62 72 74 120 122	-708921459030
SPT(16)	2142412315369408337	0 26 30 90 132 134 180 230 246 296 342 344 386 446 450 476	-481056380952
STPT(12)	2142412667578054799	0 2 30 32 42 44 90 92 102 104 132 134	-128847734490
SPT(16)	2142412767409830263	0 6 14 60 134 140 186 200 204 218 264 270 344 390 398 404	-29015959026
SPT(16)	2142412887424005149	0 18 30 44 98 104 114 120 128 134 144 150 204 218 230 248	90998215860
TPT(14)	2142413936246381867	0 2 54 56 60 62 144 146 192 194 222 224 354 356	1139820592578
TPT(14)	2142414109892761097	0 2 54 56 84 86 120 122 150 152 162 164 180 182	1313466971808
SPT(16)	2142414172246205183	0 6 18 20 56 110 140 144 170 174 204 258 294 296 308 314	1375820415894
SPT(16)	2142414246809133907	0 12 24 102 124 130 142 154 252 264 276 282 304 382 394 406	1450383344618