Prime p₀= 2338587795284265071 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 148 2 4 2 262 2 34 2 118 2 22 2 (?)
a_n: 0 2 150 152 156 158 420 422 456 458 576 578 600 602
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: 602
Found by: Landjunge
db: batch=81, k=14, 148 4 262 34 118 22

TPT(14)	2338587044984394047	0 2 30 32 54 56 60 62 132 134 174 176 180 182	-750299871024
SPT(16)	2338587241126068013	0 30 70 124 126 204 226 280 300 354 376 454 456 510 550 580	-554158197058
STPT(10)	2338587323402825819	0 2 18 20 30 32 42 44 60 62	-471881439252
SPT(16)	2338587370286358613	0 10 64 88 94 100 108 144 154 190 198 204 210 234 288 298	-424997906458
SPT(16)	2338587415569418067	0 20 36 62 84 96 104 140 186 222 230 242 264 290 306 326	-379714847004
SPT(16)	2338587489325710613	0 58 124 126 138 168 196 198 226 228 256 286 298 300 366 424	-305958554458
SPT(16)	2338588100435569069	0 40 90 138 162 204 294 300 322 328 418 460 484 532 582 622	305151303998
STPT(12)	2338588348760812607	0 2 42 44 90 92 174 176 222 224 264 266	553476547536
STPT(10)	2338588578226004981	0 2 30 32 60 62 90 92 120 122	782941739910
TPT(14)	2338588886003328599	0 2 42 44 90 92 102 104 168 170 198 200 222 224	1090719063528
SPT(16)	2338588903072100747	0 12 50 80 90 144 146 162 164 180 182 236 246 276 314 326	1107787835676