Prime p₀= 1581359744069916539 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 172 2 4 2 82 2 16 2 16 2 (?)
a_n: 0 2 108 110 282 284 288 290 372 374 390 392 408 410
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: 410
Found by: Theadalus
db: batch=78, k=14, 106 172 4 82 16 16

SPT(16)	1581358411257966739	0 10 52 94 114 144 168 172 180 184 208 238 258 300 342 352	-1332811949800
STPT(10)	1581358479914299781	0 2 30 32 60 62 90 92 120 122	-1264155616758
SPT(16)	1581359143311235247	0 36 50 164 180 204 212 222 224 234 242 266 282 396 410 446	-600758681292
STPT(10)	1581359326050099119	0 2 18 20 30 32 42 44 60 62	-418019817420
SPT(16)	1581359434180281361	0 40 78 100 106 112 126 162 166 202 216 222 228 250 288 328	-309889635178
SPT(16)	1581359686783608359	0 8 14 42 60 108 140 144 158 162 194 242 260 288 294 302	-57286308180
TPT(14)	1581359986883263121	0 2 36 38 66 68 78 80 96 98 108 110 120 122	242813346582
STPT(10)	1581360452438450909	0 2 30 32 120 122 210 212 240 242	708368534370
SPT(16)	1581360595572601267	0 30 40 46 76 84 90 114 172 196 202 210 240 246 256 286	851502684728
SPT(16)	1581360708726132553	0 18 58 76 108 126 148 150 154 156 178 196 228 246 286 304	964656216014
SPT(16)	1581360762688145657	0 14 26 30 66 80 84 144 176 236 240 254 290 294 306 320	1018618229118