Prime p₀= 1074032082680696849 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 10 2 16 2 70 2 136 2 28 2 (?)
a_n: 0 2 78 80 90 92 108 110 180 182 318 320 348 350
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: 350
Found by: Theadalus
db: batch=76, k=14, 76 10 16 70 136 28

STPT(10)	1074030969521611721	0 2 6 8 48 50 90 92 96 98	-1113159085128
STPT(10)	1074031234402426187	0 2 24 26 42 44 60 62 84 86	-848278270662
SPT(16)	1074031400061184231	0 6 36 66 72 88 148 150 238 240 300 316 322 352 382 388	-682619512618
STPT(10)	1074031413173412437	0 2 42 44 72 74 102 104 144 146	-669507284412
SPT(16)	1074031658399902957	0 6 16 60 72 82 84 126 130 172 174 184 196 240 250 256	-424280793892
SPT(16)	1074031690816823723	0 20 36 56 74 90 116 134 150 168 194 210 228 248 264 284	-391863873126
STPT(10)	1074032218255170479	0 2 48 50 90 92 132 134 180 182	135574473630
SPT(18)	1074032399859694361	0 20 30 32 50 60 62 98 108 182 192 228 230 240 258 260 270 290	317178997512
TPT(14)	1074032736466652159	0 2 30 32 138 140 168 170 288 290 330 332 420 422	653785955310
STPT(10)	1074033037087503089	0 2 42 44 60 62 78 80 120 122	954406806240
SPT(16)	1074033060684021869	0 2 14 44 78 120 158 204 308 354 392 434 468 498 510 512	978003325020