Prime p₀= 2396218144844644667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 28 2 46 2 82 2 46 2 (?)
a_n: 0 2 30 32 42 44 72 74 120 122 204 206 252 254
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: 254
Found by: Boliver
db: batch=81, k=14, 28 10 28 46 82 46

TPT(14)	2396215702558199657	0 2 114 116 132 134 174 176 300 302 312 314 330 332	-2442286445010
STPT(10)	2396216450631603371	0 2 36 38 78 80 120 122 156 158	-1694213041296
TPT(14)	2396217190263844877	0 2 24 26 42 44 72 74 114 116 150 152 210 212	-954580799790
SPT(16)	2396217232682785651	0 16 42 46 88 130 132 142 156 166 168 210 252 256 282 298	-912161859016
SPT(16)	2396217937273152221	0 6 8 20 26 42 60 78 80 98 116 132 138 150 152 158	-207571492446
STPT(10)	2396218053502730057	0 2 12 14 42 44 72 74 84 86	-91341914610
SPT(16)	2396218282585294877	0 2 6 24 72 120 132 134 162 164 176 224 272 290 294 296	137740650210
TPT(14)	2396218370515816331	0 2 78 80 210 212 258 260 300 302 378 380 408 410	225671171664
SPT(16)	2396218830506178709	0 40 48 70 72 78 82 108 292 318 322 328 330 352 360 400	685661534042
SPT(16)	2396218852983279041	0 2 12 56 60 68 72 90 98 116 120 128 132 176 186 188	708138634374
SPT(16)	2396218881063787397	0 30 44 116 204 210 242 254 282 294 326 332 420 492 506 536	736219142730