Prime p₀= 1088500425312942701 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 82 2 16 2 28 2 106 2 22 2 (?)
a_n: 0 2 36 38 120 122 138 140 168 170 276 278 300 302
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: 302
Found by: Theadalus
db: batch=76, k=14, 34 82 16 28 106 22

SPT(16)	1088499063037809217	0 4 22 34 40 72 112 126 160 174 214 246 252 264 282 286	-1362275133484
SPT(16)	1088499212175477833	0 14 56 68 90 98 104 134 210 240 246 254 276 288 330 344	-1213137464868
SPT(16)	1088499254557475273	0 8 38 60 66 108 134 170 204 240 266 308 314 336 366 374	-1170755467428
SPT(16)	1088499508341088783	0 10 58 66 108 120 148 150 286 288 316 328 370 378 426 436	-916971853918
SPT(16)	1088499648751267747	0 30 36 60 96 120 130 142 234 246 256 280 316 340 346 376	-776561674954
SPT(16)	1088500032428715541	0 66 76 78 82 120 126 148 150 172 178 216 220 222 232 298	-392884227160
TPT(14)	1088500620885549899	0 2 42 44 102 104 108 110 198 200 228 230 282 284	195572607198
TPT(14)	1088500723092818039	0 2 30 32 102 104 168 170 180 182 252 254 270 272	297779875338
STPT(10)	1088501357335213277	0 2 30 32 42 44 54 56 84 86	932022270576
STPT(10)	1088501558005566371	0 2 6 8 18 20 30 32 36 38	1132692623670
SPT(16)	1088502166573384429	0 52 70 100 154 174 184 202 300 318 328 348 402 432 450 502	1741260441728