Prime p₀= 1028620069346427737 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 40 2 28 2 4 2 22 2 16 2 (?)
a_n: 0 2 12 14 54 56 84 86 90 92 114 116 132 134
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: 134
Found by: stoneageman
db: batch=76, k=14, 10 40 28 4 22 16

SPT(16)	1028618194810237019	0 2 48 50 108 164 182 192 230 240 258 314 372 374 420 422	-1874536190718
STPT(10)	1028618486664349907	0 2 30 32 42 44 54 56 84 86	-1582682077830
SPT(16)	1028618524144689757	0 12 76 96 100 102 112 126 130 144 154 156 160 180 244 256	-1545201737980
TPT(14)	1028618691469147697	0 2 42 44 144 146 174 176 252 254 282 284 294 296	-1377877280040
STPT(10)	1028619070269923981	0 2 36 38 78 80 120 122 156 158	-999076503756
STPT(10)	1028619490660624529	0 2 18 20 30 32 42 44 60 62	-578685803208
SPT(16)	1028620298603976139	0 22 78 84 112 130 132 178 204 250 252 270 298 304 360 382	229257548402
SPT(16)	1028620597795409791	0 112 148 168 196 198 216 222 226 232 250 252 280 300 336 448	528448982054
SPT(16)	1028620684446881297	0 50 92 126 132 140 162 182 210 230 252 260 266 300 342 392	615100453560
STPT(10)	1028620691384098229	0 2 18 20 30 32 42 44 60 62	622037670492
SPT(16)	1028620771825476217	0 40 42 114 120 124 142 156 190 204 222 226 232 304 306 346	702479048480