Prime p₀= 1013557714175326811 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 70 2 58 2 94 2 22 2 16 2 (?)
a_n: 0 2 78 80 150 152 210 212 306 308 330 332 348 350
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: 350
Found by: Spectrum
db: batch=76, k=14, 76 70 58 94 22 16

SPT(16)	1013556714933041359	0 28 34 114 120 124 148 168 190 210 234 238 244 324 330 358	-999242285452
SPT(16)	1013556732753126091	0 18 48 70 76 82 90 102 106 118 126 132 138 160 190 208	-981422200720
STPT(10)	1013556928111616477	0 2 30 32 42 44 54 56 84 86	-786063710334
SPT(16)	1013556997026911611	0 36 72 82 106 108 138 148 270 280 310 312 336 346 382 418	-717148415200
SPT(16)	1013557032993957709	0 10 24 52 54 78 88 102 130 144 154 178 180 208 222 232	-681181369102
SPT(16)	1013557079438589821	0 66 108 116 188 218 248 252 266 270 300 330 402 410 452 518	-634736736990
TPT(14)	1013557822190752637	0 2 12 14 42 44 84 86 162 164 192 194 390 392	108015425826
STPT(10)	1013557976065034357	0 2 24 26 42 44 60 62 84 86	261889707546
SPT(16)	1013557991664351191	0 18 48 50 86 90 92 102 116 126 128 132 168 170 200 218	277489024380
STPT(10)	1013558082221305727	0 2 12 14 42 44 72 74 84 86	368045978916
STPT(10)	1013558521347159377	0 2 42 44 72 74 102 104 144 146	807171832566