Prime p₀= 1296902609428791191 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 136 2 70 2 106 2 58 2 40 2 34 2 (?)
a_n: 0 2 138 140 210 212 318 320 378 380 420 422 456 458
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: 458
Found by: Cruncher Pete
db: batch=77, k=14, 136 70 106 58 40 34

SPT(16)	1296902223465339313	0 16 54 60 144 174 196 210 214 228 250 280 364 370 408 424	-385963451878
STPT(10)	1296902263994715419	0 2 18 20 30 32 42 44 60 62	-345434075772
STPT(10)	1296902287159109747	0 2 30 32 42 44 54 56 84 86	-322269681444
STPT(10)	1296902392959894779	0 2 42 44 60 62 78 80 120 122	-216468896412
STPT(10)	1296902396224358177	0 2 42 44 72 74 102 104 144 146	-213204433014
STPT(10)	1296902577884862197	0 2 30 32 42 44 54 56 84 86	-31543928994
SPT(16)	1296902742675954539	0 42 48 98 110 114 138 192 230 284 308 312 324 374 380 422	133247163348
STPT(10)	1296903164622666449	0 2 30 32 60 62 90 92 120 122	555193875258
SPT(16)	1296903287015662063	0 78 118 136 138 150 196 238 288 330 376 388 390 408 448 526	677586870872
TPT(14)	1296904011363498281	0 2 18 20 30 32 78 80 168 170 198 200 210 212	1401934707090
SPT(16)	1296904136765408557	0 12 40 42 46 52 60 66 130 136 144 150 154 156 184 196	1527336617366