Prime p₀= 968914645108175501 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 34 2 82 2 28 2 64 2 40 2 (?)
a_n: 0 2 30 32 66 68 150 152 180 182 246 248 288 290
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: 290
Found by: stoneageman
db: batch=76, k=14, 28 34 82 28 64 40

SPT(16)	968913082185151517	0 30 50 66 84 116 152 182 264 294 330 362 380 396 416 446	-1562923023984
TPT(14)	968913683799339977	0 2 12 14 24 26 30 32 54 56 114 116 210 212	-961308835524
SPT(16)	968914111952228077	0 10 42 54 94 96 150 174 262 286 340 342 382 394 426 436	-533155947424
TPT(14)	968914333497024839	0 2 42 44 138 140 168 170 222 224 240 242 378 380	-311611150662
STPT(10)	968914396568432981	0 2 6 8 18 20 30 32 36 38	-248539742520
STPT(10)	968914641329081231	0 2 36 38 78 80 120 122 156 158	-3779094270
SPT(16)	968914669178431163	0 6 68 86 90 114 116 126 158 168 170 194 198 216 278 284	24070255662
STPT(10)	968915015974564661	0 2 30 32 60 62 90 92 120 122	370866389160
STPT(12)	968915063293150397	0 2 30 32 54 56 90 92 114 116 144 146	418184974896
STPT(10)	968915164207856027	0 2 30 32 42 44 54 56 84 86	519099680526
SPT(16)	968915690757960193	0 34 76 94 100 108 114 120 154 160 166 174 180 198 240 274	1045649784692