Prime p₀= 2806581687331994987 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 70 2 88 2 64 2 10 2 88 2 (?)
a_n: 0 2 42 44 114 116 204 206 270 272 282 284 372 374
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: 374
Found by: JayPi
db: batch=82, k=14, 40 70 88 64 10 88

SPT(16)	2806579951116808561	0 10 22 28 30 60 106 112 186 192 238 268 270 276 288 298	-1736215186426
SPT(16)	2806580031221411663	0 8 18 30 66 150 168 176 228 236 254 338 374 386 396 404	-1656110583324
SPT(16)	2806580052491271893	0 48 68 78 104 210 218 300 314 396 404 510 536 546 566 614	-1634840723094
SPT(16)	2806580084566830613	0 30 46 60 96 156 166 178 216 228 238 298 334 348 364 394	-1602765164374
STPT(10)	2806581413535149597	0 2 12 14 42 44 72 74 84 86	-273796845390
SPT(16)	2806581563711620601	0 18 26 32 56 60 86 92 96 102 128 132 156 162 170 188	-123620374386
SPT(16)	2806581687359616473	0 24 38 90 146 164 194 228 236 270 300 318 374 426 440 464	27621486
SPT(16)	2806582354715526823	0 10 28 34 36 60 64 66 88 90 94 118 120 126 144 154	667383531836
STPT(10)	2806582459575561059	0 2 42 44 120 122 198 200 240 242	772243566072
STPT(10)	2806582533162247751	0 2 6 8 18 20 30 32 36 38	845830252764
SPT(16)	2806582564536862963	0 40 70 76 78 90 106 144 190 228 244 256 258 264 294 334	877204867976