Prime p₀= 2338581935762299937 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 148 2 112 2 94 2 40 2 10 2 4 2 (?)
a_n: 0 2 150 152 264 266 360 362 402 404 414 416 420 422
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: 422
Found by: Landjunge
db: batch=81, k=14, 148 112 94 40 10 4

TPT(14)	2338581017549974649	0 2 12 14 102 104 132 134 180 182 240 242 390 392	-918212325288
STPT(10)	2338581168579536339	0 2 18 20 30 32 42 44 60 62	-767182763598
STPT(10)	2338581421622947619	0 2 18 20 30 32 42 44 60 62	-514139352318
SPT(16)	2338581427433716489	0 10 30 82 118 142 162 198 244 280 300 324 360 412 432 442	-508328583448
STPT(10)	2338581660877344107	0 2 30 32 42 44 54 56 84 86	-274884955830
STPT(10)	2338581914716440227	0 2 42 44 102 104 162 164 204 206	-21045859710
STPT(10)	2338581997013381237	0 2 30 32 42 44 54 56 84 86	61251081300
SPT(16)	2338582483724447581	0 18 78 88 102 106 118 196 222 300 312 316 330 340 400 418	547962147644
SPT(16)	2338582497764919643	0 4 28 40 76 108 118 144 160 186 196 228 264 276 300 304	562002619706
TPT(14)	2338582550647533857	0 2 42 44 84 86 102 104 120 122 132 134 144 146	614885233920
SPT(16)	2338583037845798399	0 8 12 80 84 90 108 132 140 164 182 188 192 260 264 272	1102083498462