Prime p₀= 2327730516521402051 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 58 2 22 2 124 2 28 2 10 2 (?)
a_n: 0 2 36 38 96 98 120 122 246 248 276 278 288 290
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: Landjunge
db: batch=81, k=14, 34 58 22 124 28 10

TPT(14)	2327728606687194047	0 2 120 122 192 194 204 206 234 236 240 242 372 374	-1909834208004
SPT(16)	2327728672722497881	0 16 18 36 48 88 102 162 166 226 240 280 292 310 312 328	-1843798904170
STPT(10)	2327729232043740821	0 2 6 8 18 20 30 32 36 38	-1284477661230
SPT(16)	2327729440205424413	0 26 36 74 86 110 138 140 174 176 204 228 240 278 288 314	-1076315977638
SPT(16)	2327729829330770983	0 48 70 76 94 138 150 154 180 184 196 240 258 264 286 334	-687190631068
SPT(16)	2327729962052725381	0 22 30 76 120 142 162 172 186 196 216 238 282 328 336 358	-554468676670
SPT(16)	2327730687655699693	0 30 48 90 156 184 190 258 316 384 390 418 484 526 544 574	171134297642
STPT(10)	2327730697958025317	0 2 12 14 42 44 72 74 84 86	181436623266
STPT(10)	2327730974833435229	0 2 42 44 60 62 78 80 120 122	458312033178
SPT(16)	2327730978973556473	0 48 66 78 94 100 108 150 154 196 204 210 226 238 256 304	462452154422
STPT(10)	2327731198443549947	0 2 42 44 72 74 102 104 144 146	681922147896