Prime p₀= 1588458736608503531 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 70 2 46 2 88 2 40 2 34 2 (?)
a_n: 0 2 48 50 120 122 168 170 258 260 300 302 336 338
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: 338
Found by: Laurent Cheylat
db: batch=78, k=14, 46 70 46 88 40 34

SPT(16)	1588457790658492813	0 36 66 90 94 108 138 178 276 316 346 360 364 388 418 454	-945950010718
SPT(16)	1588457894541196709	0 20 38 60 72 132 144 158 174 188 200 260 272 294 312 332	-842067306822
SPT(16)	1588457942774135683	0 34 64 90 106 130 178 196 228 246 294 318 334 360 390 424	-793834367848
SPT(16)	1588457963300119741	0 12 40 48 82 102 112 126 172 186 196 216 250 258 286 298	-773308383790
STPT(10)	1588457972587516991	0 2 36 38 78 80 120 122 156 158	-764020986540
STPT(10)	1588457994561663521	0 2 6 8 18 20 30 32 36 38	-742046840010
TPT(14)	1588459017949572887	0 2 60 62 180 182 240 242 282 284 354 356 420 422	281341069356
SPT(16)	1588459138675602311	0 20 62 152 188 210 216 228 230 242 248 270 306 396 438 458	402067098780
SPT(16)	1588459299459129901	0 6 18 30 52 90 136 156 172 192 238 276 298 310 322 328	562850626370
SPT(16)	1588459449400247737	0 4 54 60 82 84 106 112 144 150 172 174 196 202 252 256	712791744206
STPT(10)	1588459555017712847	0 2 30 32 42 44 54 56 84 86	818409209316