Prime p₀= 3031920509023903457 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 28 2 130 2 4 2 130 2 (?)
a_n: 0 2 30 32 42 44 72 74 204 206 210 212 342 344
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: 344
Found by: [SG-FC] hl
db: batch=82, k=14, 28 10 28 130 4 130

SPT(16)	3031919717345044573	0 10 36 40 54 78 124 130 144 150 196 220 234 238 264 274	-791678858884
STPT(12)	3031919964646814639	0 2 30 32 72 74 138 140 180 182 210 212	-544377088818
SPT(16)	3031919973698378881	0 6 16 72 88 100 192 198 280 286 378 390 406 462 472 478	-535325524576
SPT(16)	3031920086894861093	0 50 86 96 170 176 200 240 416 456 480 486 560 570 606 656	-422129042364
SPT(13)	3031920245205784861	0 12 18 48 60 78 90 102 120 132 162 168 180	-263818118596
STPT(10)	3031920411925004651	0 2 6 8 18 20 30 32 36 38	-97098898806
SPT(16)	3031920722846129567	0 24 50 102 116 162 246 264 272 290 374 420 434 486 512 536	213822226110
STPT(10)	3031920821696801849	0 2 42 44 90 92 138 140 180 182	312672898392
STPT(10)	3031920932209835201	0 2 6 8 48 50 90 92 96 98	423185931744
STPT(10)	3031921015181616461	0 2 36 38 78 80 120 122 156 158	506157713004
STPT(10)	3031921067149017191	0 2 30 32 78 80 126 128 156 158	558125113734