Prime p₀= 793591295571332747 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 34 2 88 2 40 2 16 2 82 2 (?)
a_n: 0 2 24 26 60 62 150 152 192 194 210 212 294 296
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: 296
Found by: Conan
db: batch=73, k=14, 22 34 88 40 16 82

SPT(16)	793590878666178973	0 28 30 48 64 76 78 84 100 106 108 120 136 154 156 184	-416905153774
SPT(16)	793590936715296689	0 2 8 30 60 78 90 128 144 182 194 212 242 264 270 272	-358856036058
SPT(16)	793591004259840947	0 12 20 42 54 102 116 122 174 180 194 242 254 276 284 296	-291311491800
SPT(16)	793591192528057289	0 42 80 114 210 218 224 260 282 318 324 332 428 462 500 542	-103043275458
SPT(16)	793591194796453349	0 8 14 44 60 128 150 164 168 182 204 272 288 318 324 332	-100774879398
SPT(16)	793591214519733031	0 22 76 132 136 138 162 168 370 376 400 402 406 462 516 538	-81051599716
SPT(18)	793591323110057503	0 54 78 114 124 126 154 180 226 258 304 330 358 360 370 406 430 484	27538724756
TPT(14)	793592567951375111	0 2 78 80 168 170 210 212 216 218 306 308 330 332	1272380042364
STPT(10)	793592708199670409	0 2 18 20 30 32 42 44 60 62	1412628337662
SPT(16)	793593107375118733	0 60 78 88 118 148 166 196 258 288 306 336 366 376 394 454	1811803785986
SPT(16)	793593249463783969	0 18 48 78 118 142 148 172 228 252 258 282 322 352 382 400	1953892451222