Prime p₀= 2217686536712987069 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 58 2 28 2 40 2 106 2 40 2 (?)
a_n: 0 2 30 32 90 92 120 122 162 164 270 272 312 314
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: Penguin
db: batch=81, k=14, 28 58 28 40 106 40

TPT(14)	2217685688042578907	0 2 84 86 102 104 114 116 150 152 264 266 360 362	-848670408162
STPT(10)	2217685870948202927	0 2 30 32 42 44 54 56 84 86	-665764784142
SPT(16)	2217686215231600189	0 10 40 42 48 52 94 118 174 198 240 244 250 252 282 292	-321481386880
SPT(16)	2217686330301872747	0 36 56 62 116 132 176 182 204 210 254 270 324 330 350 386	-206411114322
STPT(10)	2217686514698660567	0 2 42 44 72 74 102 104 144 146	-22014326502
SPT(16)	2217686530448502439	0 28 58 72 102 160 162 198 244 280 282 340 370 384 414 442	-6264484630
SPT(16)	2217686722183610303	0 30 38 120 168 176 198 204 260 266 288 296 344 426 434 464	185470623234
SPT(16)	2217687401993345257	0 10 24 30 52 70 72 82 192 202 204 222 244 250 264 274	865280358188
SPT(16)	2217687582556080113	0 6 26 48 66 90 114 138 206 230 254 278 296 318 338 344	1045843093044
SPT(16)	2217687924358815257	0 20 26 114 164 174 180 192 254 266 272 282 332 420 426 446	1387645828188
STPT(10)	2217688486590558341	0 2 6 8 48 50 90 92 96 98	1949877571272