Prime p₀= 2806582865618148359 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 10 2 16 2 10 2 46 2 40 2 (?)
a_n: 0 2 108 110 120 122 138 140 150 152 198 200 240 242
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: 242
Found by: JayPi
db: batch=82, k=14, 106 10 16 10 46 40

TPT(14)	2806581687331994987	0 2 42 44 114 116 204 206 270 272 282 284 372 374	-1178286153372
SPT(16)	2806581687359616473	0 24 38 90 146 164 194 228 236 270 300 318 374 426 440 464	-1178258531886
SPT(16)	2806582354715526823	0 10 28 34 36 60 64 66 88 90 94 118 120 126 144 154	-510902621536
STPT(10)	2806582459575561059	0 2 42 44 120 122 198 200 240 242	-406042587300
STPT(10)	2806582533162247751	0 2 6 8 18 20 30 32 36 38	-332455900608
SPT(16)	2806582564536862963	0 40 70 76 78 90 106 144 190 228 244 256 258 264 294 334	-301081285396
SPT(18)	2806582876900153343	0 48 90 110 116 126 188 198 248 258 308 318 380 390 396 416 458 506	11282004984
SPT(16)	2806583066054026601	0 12 62 80 116 132 140 146 192 198 206 222 258 276 326 338	200435878242
SPT(16)	2806583360678794357	0 12 22 34 72 82 96 136 180 220 234 244 282 294 304 316	495060645998
SPT(16)	2806583578894327613	0 50 56 80 108 120 140 146 168 174 194 206 234 258 264 314	713276179254
STPT(10)	2806583709739215797	0 2 30 32 42 44 54 56 84 86	844121067438