Prime p₀= 1040123697221309759 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 70 2 34 2 40 2 46 2 40 2 (?)
a_n: 0 2 60 62 132 134 168 170 210 212 258 260 300 302
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: [SG-2W]Kurzer
db: batch=76, k=14, 58 70 34 40 46 40

STPT(10)	1040122672127521181	0 2 78 80 108 110 138 140 216 218	-1025093788578
STPT(10)	1040122750224194639	0 2 30 32 60 62 90 92 120 122	-946997115120
SPT(16)	1040122765698723991	0 16 36 42 78 100 126 168 190 232 258 280 316 322 342 358	-931522585768
SPT(16)	1040123221514365669	0 4 24 42 52 72 88 94 108 114 130 150 160 178 198 202	-475706944090
SPT(16)	1040123296091425151	0 8 26 36 42 50 60 72 116 128 138 146 152 162 180 188	-401129884608
SPT(16)	1040123486954104913	0 38 78 98 110 170 210 254 330 374 414 474 486 506 546 584	-210267204846
SPT(16)	1040123835615641423	0 8 36 38 80 84 86 104 150 168 170 174 216 218 246 254	138394331664
STPT(10)	1040123850925827131	0 2 36 38 78 80 120 122 156 158	153704517372
SPT(16)	1040123990549234189	0 48 140 152 162 174 218 224 258 264 308 320 330 342 434 482	293327924430
STPT(10)	1040124752422744367	0 2 30 32 42 44 54 56 84 86	1055201434608
STPT(10)	1040124921470566037	0 2 30 32 42 44 54 56 84 86	1224249256278