Prime p₀= 1257842646980786561 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 10 2 64 2 40 2 28 2 58 2 (?)
a_n: 0 2 48 50 60 62 126 128 168 170 198 200 258 260
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: 260
Found by: Theadalus
db: batch=77, k=14, 46 10 64 40 28 58

TPT(14)	1257841429675722041	0 2 126 128 138 140 150 152 168 170 300 302 306 308	-1217305064520
STPT(10)	1257841876268937101	0 2 6 8 18 20 30 32 36 38	-770711849460
STPT(10)	1257841933144358201	0 2 6 8 48 50 90 92 96 98	-713836428360
SPT(16)	1257842088334250873	0 54 104 116 138 150 158 180 194 216 224 236 258 270 320 374	-558646535688
SPT(16)	1257842114903477941	0 12 40 76 102 148 160 166 252 258 270 316 342 378 406 418	-532077308620
SPT(16)	1257842198350438973	0 30 44 48 54 90 98 114 140 156 164 200 206 210 224 254	-448630347588
STPT(10)	1257842767277331407	0 2 30 32 42 44 54 56 84 86	120296544846
SPT(20)	1257842773046451859	0 22 42 54 112 130 144 154 172 220 222 270 288 298 312 330 388 400 420 442	126065665298
SPT(16)	1257842812395341243	0 30 54 56 60 66 80 110 114 144 158 164 168 170 194 224	165414554682
TPT(14)	1257842885894830559	0 2 42 44 102 104 120 122 132 134 198 200 228 230	238914043998
SPT(16)	1257843031090648111	0 22 28 36 72 90 102 148 180 226 238 256 292 300 306 328	384109861550