Prime p₀= 2540262587599763597 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 70 2 10 2 58 2 4 2 58 2 (?)
a_n: 0 2 30 32 102 104 114 116 174 176 180 182 240 242
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: 242
Found by: Paul
db: batch=82, k=14, 28 70 10 58 4 58

STPT(10)	2540261049674891729	0 2 18 20 30 32 42 44 60 62	-1537924871868
SPT(16)	2540261063824932377	0 24 54 80 86 90 96 144 152 200 206 210 216 242 272 296	-1523774831220
STPT(10)	2540261211009672749	0 2 18 20 30 32 42 44 60 62	-1376590090848
SPT(16)	2540261452908001787	0 12 32 72 104 110 116 152 174 210 216 222 254 294 314 326	-1134691761810
STPT(10)	2540261771115230711	0 2 6 8 48 50 90 92 96 98	-816484532886
SPT(16)	2540262281066262013	0 4 6 34 66 70 88 118 126 156 174 178 210 238 240 244	-306533501584
SPT(16)	2540262789683111081	0 26 36 80 98 108 140 200 246 306 338 348 366 410 420 446	202083347484
STPT(10)	2540262809758823267	0 2 24 26 42 44 60 62 84 86	222159059670
STPT(10)	2540263699742840681	0 2 36 38 78 80 120 122 156 158	1112143077084
SPT(16)	2540263731181975171	0 28 42 46 58 72 76 88 90 102 106 120 132 136 150 178	1143582211574
SPT(16)	2540264201811760681	0 90 112 136 148 160 192 222 316 346 378 390 402 426 448 538	1614211997084