Prime p₀= 2396300785899263627 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 136 2 88 2 10 2 10 2 16 2 (?)
a_n: 0 2 42 44 180 182 270 272 282 284 294 296 312 314
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: 314
Found by: kashi
db: batch=81, k=14, 40 136 88 10 10 16

TPT(14)	2396298991888644221	0 2 30 32 120 122 150 152 318 320 348 350 390 392	-1794010619406
STPT(10)	2396299113013487321	0 2 6 8 48 50 90 92 96 98	-1672885776306
STPT(10)	2396299242907787447	0 2 24 26 42 44 60 62 84 86	-1542991476180
SPT(16)	2396299247703753803	0 56 66 78 108 134 138 146 168 176 180 206 236 248 258 314	-1538195509824
STPT(10)	2396299910118469517	0 2 30 32 42 44 54 56 84 86	-875780794110
SPT(16)	2396300196072550871	0 8 12 26 42 50 110 138 140 168 228 236 252 266 270 278	-589826712756
SPT(16)	2396300842980733841	0 8 20 36 38 42 48 78 80 110 116 120 122 138 150 158	57081470214
SPT(16)	2396301733466380589	0 48 78 90 104 114 122 128 174 180 188 198 212 224 254 302	947567116962
SPT(16)	2396302040726655167	0 30 32 36 56 60 120 144 152 176 236 240 260 264 266 296	1254827391540
STPT(10)	2396302350735921539	0 2 18 20 30 32 42 44 60 62	1564836657912
SPT(16)	2396302424328246617	0 2 32 50 60 80 102 120 122 140 162 182 192 210 240 242	1638428982990