Prime p₀= 800798308874225381 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 76 2 58 2 16 2 22 2 64 2 (?)
a_n: 0 2 30 32 108 110 168 170 186 188 210 212 276 278
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: 278
Found by: Frank [NT]
db: batch=73, k=14, 28 76 58 16 22 64

SPT(16)	800797161681674239	0 18 24 40 54 60 70 82 90 102 112 118 132 148 154 172	-1147192551142
SPT(16)	800797207250366449	0 28 48 82 90 168 172 184 198 210 214 292 300 334 354 382	-1101623858932
SPT(16)	800797601137995893	0 20 50 138 150 210 246 258 308 320 356 416 428 516 546 566	-707736229488
STPT(10)	800797648398277181	0 2 36 38 78 80 120 122 156 158	-660475948200
SPT(16)	800798067439822043	0 30 50 54 60 96 128 140 174 186 218 254 260 264 284 314	-241434403338
SPT(16)	800798223697051189	0 30 84 88 114 198 234 250 252 268 304 388 414 418 472 502	-85177174192
SPT(16)	800798405090791441	0 10 28 88 96 126 178 180 208 210 262 292 300 360 378 388	96216566060
SPT(16)	800798591202698219	0 50 68 150 152 162 182 200 420 438 458 468 470 552 570 620	282328472838
SPT(16)	800798615304433331	0 6 32 66 68 78 92 152 216 276 290 300 302 336 362 368	306430207950
STPT(10)	800798823123136037	0 2 54 56 72 74 90 92 144 146	514248910656
SPT(16)	800798852060011523	0 66 80 108 116 134 144 168 176 200 210 228 236 264 278 344	543185786142