Prime p₀= 798846275382341141 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 34 2 28 2 70 2 100 2 88 2 (?)
a_n: 0 2 60 62 96 98 126 128 198 200 300 302 390 392
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: 392
Found by: [SG-2W]Kurzer
db: batch=73, k=14, 58 34 28 70 100 88

SPT(16)	798845561515636619	0 20 32 50 92 144 152 174 188 210 218 270 312 330 342 362	-713866704522
SPT(16)	798845603022028097	0 44 50 60 84 92 182 222 242 282 372 380 404 414 420 464	-672360313044
SPT(18)	798845849499720203	0 18 44 56 84 86 90 110 126 158 174 194 198 200 228 240 266 284	-425882620938
STPT(10)	798846149244981287	0 2 90 92 102 104 114 116 204 206	-126137359854
SPT(16)	798846176775844723	0 16 18 30 78 96 136 166 168 198 238 256 304 316 318 334	-98606496418
STPT(10)	798846220184660741	0 2 36 38 78 80 120 122 156 158	-55197680400
SPT(16)	798846365161711211	0 36 38 48 50 80 120 206 210 296 336 366 368 378 380 416	89779370070
STPT(10)	798846438709709099	0 2 48 50 90 92 132 134 180 182	163327367958
SPT(16)	798846608768675993	0 8 44 66 86 110 170 194 210 234 294 318 338 360 396 404	333386334852
TPT(14)	798847321454859401	0 2 48 50 90 92 96 98 180 182 270 272 306 308	1046072518260
STPT(12)	798847443798609239	0 2 138 140 180 182 240 242 282 284 420 422	1168416268098