Prime p₀= 2623732830737432369 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 130 2 46 2 130 2 166 2 76 2 28 2 (?)
a_n: 0 2 132 134 180 182 312 314 480 482 558 560 588 590
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: 590
Found by: [SG-FC] hl
db: batch=82, k=14, 130 46 130 166 76 28

SPT(16)	2623732260896109887	0 20 30 32 96 110 132 140 156 164 186 200 264 266 276 296	-569841322482
TPT(14)	2623732377674193389	0 2 30 32 132 134 198 200 270 272 282 284 378 380	-453063238980
STPT(10)	2623732532887149977	0 2 42 44 72 74 102 104 144 146	-297850282392
SPT(16)	2623732558235581211	0 6 72 90 108 110 128 132 146 150 168 170 188 206 272 278	-272501851158
SPT(16)	2623732624546213967	0 56 62 72 114 204 222 230 246 254 272 362 404 414 420 476	-206191218402
SPT(16)	2623732777461695909	0 14 18 84 92 140 158 182 210 234 252 300 308 374 378 392	-53275736460
STPT(10)	2623733422238001179	0 2 78 80 120 122 162 164 240 242	591500568810
STPT(10)	2623734124574769551	0 2 36 38 78 80 120 122 156 158	1293837337182
STPT(10)	2623734169513680269	0 2 12 14 90 92 168 170 180 182	1338776247900
SPT(16)	2623734305019420233	0 18 120 134 200 216 236 266 348 378 398 414 480 494 596 614	1474281987864
SPT(16)	2623734829540046693	0 84 98 104 146 174 198 216 338 356 380 408 450 456 470 554	1998802614324