Prime p₀= 2044864055156126849 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 34 2 100 2 28 2 40 2 76 2 (?)
a_n: 0 2 72 74 108 110 210 212 240 242 282 284 360 362
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: 362
Found by: matsu_pl
db: batch=80, k=14, 70 34 100 28 40 76

SPT(16)	2044861621347169223	0 20 44 54 84 98 110 126 158 174 186 200 230 240 264 284	-2433808957626
STPT(10)	2044862155521326357	0 2 60 62 72 74 84 86 144 146	-1899634800492
SPT(16)	2044862661773148439	0 22 48 52 82 94 150 190 192 232 288 300 330 334 360 382	-1393382978410
SPT(16)	2044863054352935979	0 10 22 42 60 82 108 112 180 184 210 232 250 270 282 292	-1000803190870
STPT(10)	2044863555891764681	0 2 66 68 108 110 150 152 216 218	-499264362168
STPT(10)	2044863586855842419	0 2 18 20 30 32 42 44 60 62	-468300284430
SPT(16)	2044864062811425187	0 22 70 82 100 154 184 210 304 330 360 414 432 444 492 514	7655298338
SPT(16)	2044864240086976513	0 100 130 196 214 228 234 244 270 280 286 300 318 384 414 514	184930849664
STPT(10)	2044864252144684571	0 2 96 98 168 170 240 242 336 338	196988557722
SPT(16)	2044864604357897513	0 8 14 48 98 120 140 144 200 204 224 246 296 330 336 344	549201770664
SPT(16)	2044864709394052111	0 18 42 48 90 102 126 142 156 172 196 208 250 256 280 298	654237925262