Prime p₀= 798713329047074891 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 88 2 28 2 82 2 16 2 10 2 (?)
a_n: 0 2 36 38 126 128 156 158 240 242 258 260 270 272
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: 272
Found by: [SG-2W]Kurzer
db: batch=73, k=14, 34 88 28 82 16 10

SPT(16)	798712177178638729	0 18 40 42 52 94 102 108 154 160 168 210 220 222 244 262	-1151868436162
STPT(10)	798712422426162611	0 2 6 8 48 50 90 92 96 98	-906620912280
SPT(16)	798712749516403121	0 30 56 72 78 86 92 122 156 186 192 200 206 222 248 278	-579530671770
SPT(16)	798712811440563181	0 16 42 70 82 96 106 126 136 156 166 180 192 220 246 262	-517606511710
STPT(10)	798713058440023169	0 2 18 20 60 62 102 104 120 122	-270607051722
STPT(10)	798713098973796197	0 2 90 92 102 104 114 116 204 206	-230073278694
SPT(16)	798713862224616673	0 4 66 70 90 126 150 174 196 220 244 280 300 304 366 370	533177541782
STPT(10)	798714303849304277	0 2 30 32 42 44 54 56 84 86	974802229386
STPT(10)	798714363240258737	0 2 30 32 42 44 54 56 84 86	1034193183846
SPT(16)	798714378190666291	0 18 60 70 72 90 120 180 190 250 280 298 300 310 352 370	1049143591400
SPT(16)	798714389950450313	0 54 74 84 110 168 200 228 236 264 296 354 380 390 410 464	1060903375422