Prime p₀= 1588459017949572887 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 118 2 58 2 40 2 70 2 64 2 (?)
a_n: 0 2 60 62 180 182 240 242 282 284 354 356 420 422
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: 422
Found by: emoga
db: batch=78, k=14, 58 118 58 40 70 64

SPT(16)	1588457894541196709	0 20 38 60 72 132 144 158 174 188 200 260 272 294 312 332	-1123408376178
SPT(16)	1588457942774135683	0 34 64 90 106 130 178 196 228 246 294 318 334 360 390 424	-1075175437204
SPT(16)	1588457963300119741	0 12 40 48 82 102 112 126 172 186 196 216 250 258 286 298	-1054649453146
STPT(10)	1588457972587516991	0 2 36 38 78 80 120 122 156 158	-1045362055896
STPT(10)	1588457994561663521	0 2 6 8 18 20 30 32 36 38	-1023387909366
TPT(14)	1588458736608503531	0 2 48 50 120 122 168 170 258 260 300 302 336 338	-281341069356
SPT(16)	1588459138675602311	0 20 62 152 188 210 216 228 230 242 248 270 306 396 438 458	120726029424
SPT(16)	1588459299459129901	0 6 18 30 52 90 136 156 172 192 238 276 298 310 322 328	281509557014
SPT(16)	1588459449400247737	0 4 54 60 82 84 106 112 144 150 172 174 196 202 252 256	431450674850
STPT(10)	1588459555017712847	0 2 30 32 42 44 54 56 84 86	537068139960
SPT(16)	1588459916711853149	0 18 48 68 74 122 132 144 188 200 210 258 264 284 314 332	898762280262