Prime p₀= 2386362994473235991 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 118 2 58 2 28 2 34 2 58 2 28 2 (?)
a_n: 0 2 120 122 180 182 210 212 246 248 306 308 336 338
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: 338
Found by: [AF>Libristes] Davlabedave
db: batch=81, k=14, 118 58 28 34 58 28

TPT(14)	2386362247985460989	0 2 12 14 72 74 102 104 138 140 228 230 312 314	-746487775002
STPT(10)	2386362255840803291	0 2 6 8 18 20 30 32 36 38	-738632432700
SPT(16)	2386362347337448999	0 22 70 72 78 102 112 154 228 270 280 304 310 312 360 382	-647135786992
STPT(10)	2386362707468269379	0 2 48 50 90 92 132 134 180 182	-287004966612
SPT(16)	2386362956008267279	0 10 28 40 42 58 82 138 142 198 222 238 240 252 270 280	-38464968712
SPT(16)	2386362967958829917	0 32 44 102 114 116 120 134 162 176 180 182 194 252 264 296	-26514406074
SPT(16)	2386363185787429291	0 46 48 76 112 130 132 136 192 196 198 216 252 280 282 328	191314193300
SPT(16)	2386363337561926727	0 2 42 60 72 110 146 174 182 210 246 284 296 314 354 356	343088690736
STPT(10)	2386363405501023209	0 2 18 20 30 32 42 44 60 62	411027787218
STPT(10)	2386364201979313091	0 2 6 8 48 50 90 92 96 98	1207506077100
STPT(10)	2386364432173684511	0 2 6 8 48 50 90 92 96 98	1437700448520