Prime p₀= 1051415171232431051 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 34 2 160 2 10 2 118 2 34 2 (?)
a_n: 0 2 60 62 96 98 258 260 270 272 390 392 426 428
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: 428
Found by: stoneageman
db: batch=76, k=14, 58 34 160 10 118 34

TPT(14)	1051413539454007187	0 2 84 86 132 134 150 152 210 212 234 236 252 254	-1631778423864
STPT(10)	1051413804096162851	0 2 36 38 78 80 120 122 156 158	-1367136268200
STPT(10)	1051413904812136427	0 2 42 44 72 74 102 104 144 146	-1266420294624
STPT(10)	1051414749517622261	0 2 30 32 78 80 126 128 156 158	-421714808790
STPT(10)	1051414853463122999	0 2 42 44 90 92 138 140 180 182	-317769308052
STPT(10)	1051415056483649951	0 2 30 32 60 62 90 92 120 122	-114748781100
SPT(16)	1051415233733004367	0 22 30 36 40 42 64 90 106 132 154 156 160 166 174 196	62500573316
STPT(10)	1051415398397750567	0 2 30 32 42 44 54 56 84 86	227165319516
SPT(16)	1051415401168104757	0 24 70 96 130 136 144 192 214 262 270 276 310 336 382 406	229935673706
SPT(16)	1051415667842773193	0 38 56 78 104 108 140 218 246 324 356 360 386 408 426 464	496610342142
SPT(16)	1051415806362872693	0 26 36 68 78 98 114 150 224 260 276 296 306 338 348 374	635130441642