Prime p₀= 2621678288737687469 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 64 2 28 2 58 2 52 2 28 2 (?)
a_n: 0 2 12 14 78 80 108 110 168 170 222 224 252 254
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: 254
Found by: [SG-2W]Kurzer
db: batch=82, k=14, 10 64 28 58 52 28

TPT(14)	2621676944053729481	0 2 6 8 36 38 78 80 96 98 108 110 150 152	-1344683957988
STPT(10)	2621676997713567317	0 2 30 32 42 44 54 56 84 86	-1291024120152
SPT(16)	2621677170461038057	0 36 60 64 90 142 174 222 274 322 354 406 432 436 460 496	-1118276649412
STPT(10)	2621677389069363017	0 2 30 32 42 44 54 56 84 86	-899668324452
SPT(16)	2621677698380001649	0 22 42 48 70 72 168 174 358 364 460 462 484 490 510 532	-590357685820
STPT(10)	2621677972105158677	0 2 60 62 72 74 84 86 144 146	-316632528792
STPT(10)	2621678568249229649	0 2 18 20 210 212 402 404 420 422	279511542180
STPT(10)	2621678605561078541	0 2 30 32 78 80 126 128 156 158	316823391072
SPT(16)	2621678728532061019	0 24 40 64 70 82 90 94 108 112 120 132 138 162 178 202	439794373550
SPT(16)	2621678891633451161	0 2 12 30 68 80 96 122 156 182 198 210 248 266 276 278	602895763692
STPT(10)	2621678996514534497	0 2 30 32 72 74 114 116 144 146	707776847028