Prime p₀= 976078809737830787 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 10 2 28 2 58 2 10 2 64 2 (?)
a_n: 0 2 60 62 72 74 102 104 162 164 174 176 240 242
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: [SG-2W]Kurzer
db: batch=76, k=14, 58 10 28 58 10 64

SPT(16)	976077647381017219	0 22 34 52 64 78 90 108 124 142 154 168 180 198 210 232	-1162356813568
TPT(14)	976078006933001351	0 2 36 38 96 98 108 110 150 152 156 158 210 212	-802804829436
TPT(14)	976078197241732577	0 2 24 26 42 44 54 56 114 116 192 194 234 236	-612496098210
SPT(16)	976078277640990257	0 32 42 56 84 132 152 156 170 174 194 242 270 284 294 326	-532096840530
STPT(12)	976078333993390907	0 2 12 14 24 26 30 32 42 44 54 56	-475744439880
SPT(18)	976078692613420183	0 28 40 64 100 118 154 156 168 286 298 300 336 354 390 414 426 454	-117124410604
SPT(16)	976079277226358573	0 6 14 20 36 56 78 80 144 146 168 188 204 210 218 224	467488527786
SPT(16)	976079429781683147	0 32 42 56 110 182 200 260 312 372 390 462 516 530 540 572	620043852360
STPT(10)	976079554075559147	0 2 30 32 42 44 54 56 84 86	744337728360
STPT(10)	976079763700284557	0 2 30 32 42 44 54 56 84 86	953962453770
SPT(16)	976079813594042189	0 44 84 92 104 120 134 152 240 258 272 288 300 308 348 392	1003856211402