Prime p₀= 3035331300415323851 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 124 2 70 2 10 2 226 2 28 2 88 2 (?)
a_n: 0 2 126 128 198 200 210 212 438 440 468 470 558 560
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: 560
Found by: [SG-FC] hl
db: batch=82, k=14, 124 70 10 226 28 88

SPT(16)	3035329797065159081	0 8 26 50 60 68 78 116 120 158 168 176 186 210 228 236	-1503350164770
STPT(10)	3035329955006113319	0 2 18 20 60 62 102 104 120 122	-1345409210532
SPT(16)	3035330187082778471	0 18 32 60 96 98 102 122 126 146 150 152 188 216 230 248	-1113332545380
SPT(16)	3035330447671804019	0 24 48 92 114 134 140 182 240 282 288 308 330 374 398 422	-852743519832
TPT(14)	3035330867835623057	0 2 30 32 54 56 72 74 84 86 180 182 204 206	-432579700794
SPT(16)	3035331029334922217	0 42 54 56 92 126 146 176 180 210 230 264 300 302 314 356	-271080401634
SPT(16)	3035331303388428437	0 26 74 84 116 120 126 144 176 194 200 204 236 246 294 320	2973104586
TPT(14)	3035331648359432111	0 2 60 62 96 98 156 158 186 188 198 200 306 308	347944108260
SPT(16)	3035332170741074341	0 12 16 82 102 130 186 208 300 322 378 406 426 492 496 508	870325750490
SPT(16)	3035332365589400753	0 8 18 24 44 74 78 86 198 206 210 240 260 266 276 284	1065174076902
STPT(10)	3035333170056178877	0 2 12 14 72 74 132 134 144 146	1869640855026