Prime p₀= 2956902863856671459 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 4 2 10 2 178 2 16 2 (?)
a_n: 0 2 30 32 72 74 78 80 90 92 270 272 288 290
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: 290
Found by: ginga
db: batch=82, k=14, 28 40 4 10 178 16

TPT(14)	2956899737050907621	0 2 108 110 138 140 150 152 156 158 276 278 288 290	-3126805763838
STPT(10)	2956900031777653187	0 2 30 32 72 74 114 116 144 146	-2832079018272
STPT(12)	2956900552660478447	0 2 72 74 84 86 90 92 102 104 174 176	-2311196193012
SPT(16)	2956901075784675977	0 84 86 96 102 156 192 200 276 284 320 374 380 390 392 476	-1788071995482
TPT(14)	2956901782368334679	0 2 102 104 138 140 240 242 258 260 462 464 468 470	-1081488336780
SPT(16)	2956901785934167567	0 6 40 52 72 126 132 136 216 220 226 280 300 312 346 352	-1077922503892
STPT(10)	2956903054001535017	0 2 30 32 42 44 54 56 84 86	190144863558
SPT(18)	2956903058135113531	0 16 22 30 42 90 96 126 198 250 322 352 358 406 418 426 432 448	194278442072
STPT(10)	2956903435529232071	0 2 36 38 78 80 120 122 156 158	571672560612
SPT(16)	2956903500940810723	0 18 24 54 130 144 186 208 276 298 340 354 430 460 466 484	637084139264
SPT(16)	2956903633926930421	0 16 42 52 66 82 100 112 126 138 156 172 186 196 222 238	770070258962