Prime p₀= 1364968170402345827 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 16 2 88 2 58 2 28 2 76 2 (?)
a_n: 0 2 24 26 42 44 132 134 192 194 222 224 300 302
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: 302
Found by: emoga
db: batch=77, k=14, 22 16 88 58 28 76

SPT(16)	1364967277392033109	0 54 82 120 132 168 172 202 210 240 244 280 292 330 358 412	-893010312718
STPT(10)	1364967478966636421	0 2 30 32 60 62 90 92 120 122	-691435709406
SPT(16)	1364967556548423161	0 6 36 38 66 78 98 102 206 210 230 242 270 272 302 308	-613853922666
SPT(16)	1364967762301678949	0 8 12 14 30 42 44 84 128 168 170 182 198 200 204 212	-408100666878
STPT(10)	1364967921036592721	0 2 30 32 60 62 90 92 120 122	-249365753106
SPT(16)	1364968098924422557	0 4 10 42 66 90 112 130 276 294 316 340 364 396 402 406	-71477923270
SPT(16)	1364968391722589779	0 24 52 54 60 112 130 154 168 192 210 262 268 270 298 322	221320243952
SPT(16)	1364968584597151789	0 10 12 40 48 58 120 192 208 280 342 352 360 388 390 400	414194805962
SPT(16)	1364968755582328079	0 78 80 84 98 144 164 212 240 288 308 354 368 372 374 452	585179982252
SPT(16)	1364968775521148807	0 14 32 36 60 80 92 102 104 114 126 146 170 174 192 206	605118802980
TPT(14)	1364968924776233549	0 2 78 80 180 182 258 260 378 380 420 422 498 500	754373887722